CENTRIFUGAL  PUMPS 


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Metallurgical  and  Chemical  Engineering  Power 


CENTRIFUGAL  PUMPS 


BY 


R.  L.  DAUGHERTY,  A.  B.,  M.  E. 

ASSISTANT    PROFESSOR   OF   HYDRAULICS,    SIBLEY    COLLEGE,    CORNELL 
UNIVERSITY.       AUTHOR    OF    "HYDRAULIC    TURBINES" 


FIRST  EDITION 


McGRAW-HILL  BOOK  COMPANY,  INC. 
239  WEST  39TH  STREET,  NEW  YORK 

6  BOUVERIE  STREET,  LONDON,  E.  C. 

1915 


^ 


COPYRIGHT,  1915,  BY  THE 
McGRAw-HiLL  BOOK  COMPANY,  INC. 


THE    MAPIiE     PRESS     YORK    PA 


PREFACE 

The  extensive  use  and  increasing  popularity  of  centrifugal 
pumping  machinery  make  it  necessary  for  many  to  become  famil- 
iar with  this  subject  in  all  its  phases.  In  this  book  an  effort  has 
been  made  to  cover  the  following  ground:  To  illustrate  and 
explain  all  the  essential  features  of  construction  of  modern  cen- 
trifugal pumps,  to  present  a  clear  and  intelligible  theory  which 
shall  be  entirely  general  in  its  nature,  to  explain  by  this  theory 
the  pump  characteristics  and  connect  the  theory  with  the  actual 
facts,  to  present  a  thorough  discussion  of  the  factors  affecting 
efficiency,  to  consider  the  characteristics  of  various  types  of  pumps 
and  their  suitability  for  different  services,  to  compare  centrifu- 
gal with  displacement  pumps,  and  to  present  various  general 
laws  and  factors  leading  to  a  better  appreciation  of  the  field  of 
service  of  such  pumps  and  a  better  means  of  selecting  the  proper 
combinations.  While  this  is  not  primarily  a  book  on  design,  it 
is  believed  that  a  thorough  study  of  the  foregoing  will  be  of 
value  to  prospective  designers,  and  in  addition  the  methods  of 
design  of  centrifugal  pumps  are  outlined. 

The  material  in  this  book  is  based  upon  a  study  of  the  per- 
formances of  123  turbine  and  51  volute  centrifugal  pumps  made 
by  17  and  12  different  companies  respectively.  The  field 
covered  by  them  ranged  from  1  to  11  stages,  heads  from  7  to  1843 
ft.,  capacities  from  108  to  132,000  gal.  per  minute,  speeds  from 
62  to  20,000  r.p.m.,  and  efficiencies  from  30  to  87  per  cent.  A 
considerable  portion  of  the  work  is  also  founded  upon  the  anal- 
ysis of  tests  made  by  the  author  upon  a  volute  pump  and  a 
turbine  pump  for  both  of  which  all  information  regarding  di- 
mensions and  other  quantities  was  obtainable.  With  the  turbine 
pump  an  extensive  and  accurate  series  of  tests  was  made  at 
various  speeds  from  700  to  2,000  r.p.m.  Both  of  these  pumps 
were  regular  commercial  pumps  of  good  design,  not  freak  pumps 
built  for  experimental  purposes  only. 

The  author  has  drawn  upon  trade  catalogues  and  several 
books  and  papers  for  much  of  his  material,  due  credit  for  which  is 
given  in  the  text,  but  it  is  believed  that  a  very  great  deal  of  the 

v 

330324 


vi  PREFACE 

following  treatise  will  be  found  to  be  new.  The  common  usage 
regarding  terms  employed  has  been  followed  as  far  as  possible, 
but  in  cases  where  there  were  no  precedents  or  where  the  usage 
was  illogical  and  confusing,  new  terms  have  been  created. 
It  is  hoped  that  eventually  some  of  these  things  may  become 
standardized. 

The  book  has  been  so  written  as  to  serve  the  needs  of  the  prac- 
tising engineer  who  wishes  to  obtain  a  grasp  of  this  subject.  By 
the  insertion  of  problems  and  questions  it  is  believed  that  it  will 
be  found  equally  well  adapted  for  use  as  a  text. 

The  author  wishes  to  express  his  gratitude  to  the  various  manu- 
facturers, whose  names  are  attached  to  the  illustrations  in  the 
book,  for  their  valuable  assistance  in  furnishing  such  material. 
He  is  also  indebted  to  Mr.  F.  G.  Switzer,  Fellow  in  Sibley  Col- 
lege, for  aid  in  performing  the  experimental  work  and  for  his 
criticism  of  the  proof. 

R.  L.  D. 

ITHACA,  N.  Y., 
January,  1915. 


CONTENTS 

PAGE 

PREFACE    v 

CHAPTER  I 

INTRODUCTION 1 

Definition — Classification — Reaction  turbine  vs.  turbine  pump — 
Historical  development — Conditions  of  use — Pump  size — Rated 
head  and  discharge. 

CHAPTER  II 

DESCRIPTION 16 

The  impeller — Diffuser — Clearance  rings — Stuffing  boxes — The 
case — Balancing. 

CHAPTER  III 

INSTALLATION  AND  OPERATION 40 

Priming — Foot  valves  and  strainers — Suction  lift — Piping  connec- 
tions— Pumps  in  series  and  in  parallel — Operating  a  centrifugal 
pump. 

CHAPTER  IV 

GENERAL  THEORY 44 

Notation — Relation  between  absolute  and  relative  velocities — 
Equation  of  continuity — General  equation  of  energy — Losses  of  J 
head  in  pipes — Head  developed  by  pump — Centrifugal  action  or 
forced  vortex — Free  vortex — Illustration  of  centrifugal  pump 
losses — Definitions  of  efficiencies — Duty — Abbreviations — Con- 
version factors — Useful  formulas — Problems. 

CHAPTER  V 

THEORY  OP  CENTRIFUGAL  PUMPS 59 

Theorem  of  angular  momentum — Torque  exerted  by  impeller — 
Power  imparted  by  impeller — Head  imparted  by  impeller — Losses    / 
of  head — Head  of  impending  delivery — Relation  between  speed,y 
head,    and    discharge — Use    of    factors — Hydraulic    efficiency — 
Maximum    hydraulic     efficiency — Maximum    gross    efficiency — 
Experimental  analysis — Effect  of  number  of  vanes — Defects  of 
the  theory — A  corrected  theory — Value  of  the  theory — Problems. 

vii 


viii  CONTENTS 

CHAPTER  VI 

PAGE 

CHARACTERISTICS 88 

Definition  of  characteristics — Description  of  pumps  tested — 
Head-discharge  curves  at  constant  speed — Power-discharge  curves 
at  constant  speed — Efficiency-discharge  curves  at  constant  speed — 
Impending  delivery  or  shut-off — Maximum  efficiency-speed — Zero 
lift  and  maximum  discharge — Constant  discharge-variable  speed — 
Constant  lift-variable  speed — Constant  static  lift  with  friction- 
variable  speed — Constant  static  lift  with  friction-constant  speed — 
Efficiency  of  pump  and  pipe  line — Characteristic  curves — Prob- 
lems. 

CHAPTER  VII 

DISK  FRICTION 107 

Definition — Theory — Experimental  results — Summary  of  results — 
Approximate  formulas — rConclusions — Problems. 

CHAPTER  VIII 

FACTORS  AFFECTING  EFFICIENCY Ill 

Efficiency  of  a  single  pump — Efficiency  of  a  series  of  pumps — Type 
of  impeller — Efficiency-capacity — Efficiency-head — Efficiency-speed 
— Efficiency-G.P.M./V^ — Efficiency-specific  speed — Pumps  with 
high  specific  speeds — Effect  of  number  of  stages — Summary 
— Problems. 

CHAPTER  IX 

CENTRIFUGAL  PUMPS  vs.  DISPLACEMENT   PUMPS.    . 128 

Relative  speeds — Comparative  size — Comparative  efficiency — 
Comparative  cost — Comparative  characteristics — Advantages  of 
centrifugal  pumps — Advantages  of  displacement  pumps — 
Problems. 

CHAPTER  X 

COMPARISON  OF  TYPES  OF  CENTRIFUGAL  PUMPS 132 

Maximum  efficiency  of  turbine  vs.  volute  pumps — Average  effi- 
ciency of  turbine  vs.  volute  pumps — Rising  vs.  falling  characteris- 
tics— Problems. 

CHAPTER  XI 

GENERAL  LAWS  AND  FACTORS 136 

General  relations — Values  of  <£  and  c  for  maximum  efficiency — 
Values  of  the  ratio  D/B — Diameter  and  discharge — Specific  speed 
— Illustrations  of  specific  speed — Determination  and  use  of  fac- 
tors— Problems. 


CONTENTS  ix 

CHAPTER  XII 

PAGE 

PUMP  TESTING 144 

Purpose  of  test — Measurement  of  head — Measurement  of  water — 
Measurement  of  speed — Measurement  of  power — Plotting  curves — 
Problems. 

CHAPTER  XIII 

COSTS 153 

Costs  of  centrifugal  pumps — Cost  of  pumping — Problems. 

CHAPTER  XIV 

ROTARY  AND  SCREW  PUMPS 158 

Rotary  pump — Screw  or  propeller  pump. 

CHAPTER  XV 

APPLICATIONS  OF  CENTRIFUGAL  PUMPS 160 

Steam  power  plants — Fire  pumps — Deep  well  pumps — Mine 
pumps — Dredging- — Waterworks — Miscellaneous  uses. 

CHAPTER  XVI 

DESIGN  OF  A  CENTRIFUGAL   PUMP 168 

Empirical  procedure — Layout  of  impeller  vanes — Layout  of  a 
mixed  flow  impeller — Rating  chart — Problems. 

APPENDIX  A 179 

Test  data. 

APPENDIX  B 183 

Review  questions. 

APPENDIX  C 187 

Table  of  3/4  powers  of  numbers. 

INDEX  .   189 


For  notation  see  page  44. 

For  abbreviations  see  page  56. 

For  conversion  factors  see  page  56. 

For  useful  formulas  see  pages  57,  137,  139. 


CENTRIFUGAL  PUMPS 

CHAPTER  I 
INTRODUCTION 

1.  Definition. — Centrifugal  pumps  are  so   called  because  of 
the  fact  that  centrifugal  force  or  the  variation  of  pressure  due 
to  rotation  is  an  important  factor  in  their  operation.     However, 
as  will  be  shown  later,  there  are  other  actions  which  have  impor- 
tant effects. 

In  brief  the  centrifugal  pump  consists  of  an  impeller  rotating 
within  a  case  as  shown  in  Fig.  1.  Water  enters  the  impeller  at 
the  center,  flows  radially  outward,  and  is  discharged  from  the 
circumference  into  the  case.  During  this  flow  through  the  im- 
peller, the  water  has  received  energy  from  the  vanes  resulting 
in  an  increase  both  in  pressure  and  velocity.  Since  a  large  part 
of  the  energy  of  the  water  at  discharge  from  the  impeller  is  kinetic, 
it  follows  that  in  any  efficient  pump  it  is  necessary  to  conserve 
this  kinetic  energy  and  transform  it  into  pressure. 

For  the  sake  of  simplicity  the  water  is  shown  as  entering  the 
impeller  in  Fig.  1  with  a  positive  pressure  by  which  is  meant  a 
pressure  that  is  greater  than  that  of  the  atmosphere.  However, 
the  pressure  at  this  point  is  usually  less  than  that  of  the  atmos- 
phere in  which  case  we  call  it  negative.  Likewise  the  axis  of 
rotation  need  not  necessarily  be  vertical  as  shown. 

2.  Classification. — Centrifugal  pumps  are  broadly  divided  into 
two  classes: 

1.  Turbine  pumps. 

2.  Volute  pumps. 

While  there  are  still  other  types,  the  two  given  are  the  most 
important  and  are  representative  of  all  the  others. 

The  turbine  pump  is  one  in  which  the  impeller  is  surrounded 
by  a  diffuser  containing  diffusion  vanes  as  shown  in  Figs.  2  and  3. 
These  provide  gradually  enlarging  passages  whose  function  it  is  to 
reduce  the  velocity  of  the  water  leaving  the  impeller  and  thus 

1 


2  CENTRIFUGAL  PUMPS 

efficiently  transform  velocity  head  into  pressure  head.  The  cas- 
ing surrounding  the  diffusion  ring  may  be  either  circular  and  con- 
centric with  the  impeller  or  it  may  be  of  a  spiral  form.  While  the 
latter  may  be  slightly  superior  from  the  standpoint  of  efficiency, 
the  cost  of  production  is  usually  slightly  greater. 


FIG.  1. — Centrifugal  pump  with  whirlpool  chamber  and  spiral  case. 

The  volute  pump  is  one  which  has  no  diffusion  vanes  but, 
instead,  the  casing  is  of  a  spiral  type  so  made  as  to  produce  an 
equal  velocity  of  flow  at  all  sections  around  the  circumference 


INTRODUCTION 


and  also  to  gradually  reduce  the  velocity  of  the  water  as  it  flows 
from  the  impeller  to  the  discharge  pipe.  Thus  the  energy  trans- 
formation is  accomplished  in  another  way.  The  spiral  is  often 


FIG.  2. — Turbine  pump  with 
circular  case. 


FIG.  3. — Turbine  pump  with 
volute  case. 


called  a  volute,  whence  the  pump  has  received  its  name.  (See 
Fig.  4.)  The  taper  portion  between  the  case  proper  and  the 
discharge  flange  is  often  called  the  nozzle. 

Occasionally  pumps  have  been  built  with  what  is  called  a 
whirlpool  chamber  as  shown  in  Fig.  1.     This  consists  of  a  ring 


FIG.  4. — Volute  pump. 

surrounding  the  impeller,  the  width  of  which,  parallel  to  the  shaft, 
is  the  same  as  that  of  the  impeller.  Since  the  water  from  the 
impeller  enters  this  space  with  a  velocity  having  a  tangential 


4  CENTRIFUGAL  PUMPS 

component,  it  may  be  seen  that  the  path  of  the  water  will  be  some 
form  of  spiral  and  that  its  velocity  will  gradually  diminish  as  it 
approaches  the  outer  circumference,  with  a  consequent  increase 
in  pressure.  This  whirlpool  chamber  is  then  surrounded  by 
either  a  circular  or  a  spiral  case  in  the  same  manner  as  the  tur- 
bine pump.  In  fact  it  is  but  little  different  from  the  turbine 
pump  except  that  the  diffusion  vanes  are  absent.  It  may  be  seen 
that  this  construction  adds  to  the  size  of  the  case  as  compared 


FIG.  5. — Two-stage  turbine  pump.      (Chicago  Pump  Co.} 


with  the  volute  pump  and  thus  makes  it  more  expensive.  Also 
unless  the  outer  diameter  of  the  whirlpool  chamber  is  large  as 
compared  with  the  inner  diameter,  the  pressure  transformation 
will  not  be  made  very  effectively.  Experimental  work  has 
indicated  that  the  actual  efficiency  of  the  whirlpool  chamber  is 
not  very  high  in  any  event.  It  is  believed  to  be  better  to  add  the 
diffusion  vanes  so  as  to  produce  the  turbine  pump,  as  the  outer 
diameter  can  then  be  materially  reduced,  while  at  the  same  time 
the  vanes  are  held  to  improve  the  efficiency.  The  whirlpool 
chamber  is,  therefore,  seldom  used  except  in  a  very  reduced 
form  with  some  volute  pumps  as  shown  in  Fig.  9.  For  these 


INTRODUCTION 


reasons  it  is  not  thought  to  be  necessary  to  consider  it  as  a 
separate  type. 

In  order  to  produce  a  cheap  pump  the  impeller  may  be  set 
concentrically  in  a  circular  case.     The  efficiency  of  such  a  pump 


FIG.  6. — Details  of  turbine  pump.     (Chicago  Pumy  Co.) 


FIG.  7. — Multi-stage  turbine  pump  with  split  case.   (Henry  R.  Worthington.) 

is  necessarily  low,  in  fact,  as  will  be  shown  later,  the  efficiency 
cannot  rise  above  50  per  cent.  Its  only  merit  is'  cheapness  of 
construction,  largely  because  the  same  case  can  be  used  for  a  large 
number  of  sizes  of  impeller. 


CENTRIFUGAL  PUMPS 


In  this  connection  it  should  be  emphasized  that  a  "  rotary 
pump"  is  not  a  centrifugal  pump.  The  rotary  pump  is  shown  in 
Fig.  99.  It  is  positive  in  its  action  and  is  essentially  a  displace- 
ment pump,  though  of  the  rotating  rather  than  the  reciprocating 
type. 

The  term  " centrifugal  pump"  will  be  understood  to  cover 
both  the  turbine  and  the  volute  pump  as  well  as  any  other  sub- 


FIG.  8. — 72-in.    double-suction    volute    pump.     (Alberger 
Pump  and  Condenser  Co.) 

ordinate  forms.  By  some  the  expression  " centrifugal  pump" 
is  restricted  in  its  meaning  to  the  volute  and  similar  types,  while 
the  first  named  is  designated  as  a  "turbine  pump."  But  as  may 
readily  be  seen,  they  differ  only  in  minor  detail  so  that  the  turbine 
pump  is  also  a  centrifugal  pump.  By  some  it  is  proposed  to 


INTRODUCTION  7 

call  them  " turbine  centrifugal  pumps"  and  "volute  centrifugal 
pumps." 

Pumps  are  also  further  classified  as  single-stage  or  multi-stage 
pumps  according  to  whether  there  is  but  one  impeller,  as  in  Fig.  9, 
or  whether  there  are  two  or  more  impellers  through  which  the 
water  flows  in  series  as  illustrated  in  Fig.  5. 


FIG.  9. — Volute    centrifugal  pump.     (Alberger  Pump  and  Condenser  Co.) 


Still  a  further  classification  may  be  made  as  to  how  the  case 
can  be  opened  up.  We  may  have  the  split  case  type  as  shown  in 
Fig.  7  or  the  side  plate  type  as  in  Fig.  9. 

Pumps  may  also  be  classified  as  horizontal  or  vertical  shaft 
types.  The  former  have  already  been  shown,  the  latter  type 
is  illustrated  in  Fig.  10.  The  latter  may  be  either  submerged 
beneath  the  water  or  it  may  be  above  the  water  level. 

Sometimes  the  distinction  is  made  as  to  whether  a  centrifugal 
pump  possesses  a  rising  or  a,  falling  characteristic.  The  latter  in 
turn  may  be  subdivided  into  flat  or  steep  characteristics.  (See 


8 


CENTRIFUGAL  PUMPS 


Fig.  11.)  By  a  rising  characteristic  is  meant  that  when  the 
pump  runs  at  constant  speed  the  head  increases  as  the  discharge 
is  increased  from  .zero.  After  a  certain  value  is  reached,  however, 
the  head  begins  to  fall  again,  A  falling  characteristic  means  that 

the  head  continuously  decreases  as 
the  discharge  increases  from  zero. 
The  meaning  of  flat  or  steep  is  readily 
seen  from  the  figure. 

Other  less  fundamental  classifica- 
tions will  be  made  throughout  the 
text. 

3.  Reaction  Turbine  vs.  Turbine 
Pump. — It  is  often  stated  that  the 
turbine  pump  is  nothing  but  a  reac- 
tion turbine  reversed,  but  such  a 
statement  may  be  misleading.  It 
is  true  that  they  have  many  things 
in  common  but  their  differences  are 
as  striking  as  their  similarities.  The 
vector  relations  of  the  velocities,  for 
instance,  are  analogous  in  the  two^ 
cases,  yet  the  actual  appearances  of 
the  velocity  diagrams  are  usually 
unlike,  since  the  relations  of  angles 
and  vane  curvature  are  different.  It 
might  be  possible  to  run  one  machine 
as  the  other  but  the  resulting  effi- 
ciency would  be  low.  It  does  not 
seem  possible  to  design  a  good  ma- 

Chine  which  sha11  be  equally,  well 
adapted  for  either  purpose  except 
at  a  considerable  sacrifice  of  efficiency. 

The  fundamental  equations  may  be  applied  alike  to  either 
type,  but  as  soon  as  certain  special  relations  are  introduced  into 
these  fundamental  equations  the  resul  t  may  be  that  the  equations 
cannot  be  used  for  both  alike. 

It  is  also  well  worth  noting  that  in  the  turbine  one  of  the  steps 
is  the  transformation  of  pressure  head  into  velocity  head,  while 
with  the  pump  we  are  concerned  with  converting  kinetic  energy 
into  pressure  energy.  The  former  operation  can  be  more  effi- 
ciently performed  than  the  latter.  Also  with  the  inward  flow 


INTRODUCTION 


9 


reaction  turbine  we  have  flow  taking  place  through  converging 
passages,  while  with  the  centrifugal  pump  the  flow  takes  place 
through  diverging  passages  with  a  resulting  instability  of  stream 
lines.  For  both  of  these  reasons  it  will  be  found  that  centrifu- 
gal pumps  have  not  attained  as  high  efficiencies  as  have  been 
reached  with  reaction  turbines. 


130 


120 


110 


100 


SO 


70 


50 


FlatjCha 


Speed  Constant 


istic. 


racter 


stic- 


0         10        20        30        40        50        60        70        80        90       100      UO      120      130     140 
Percent  of  Normal  Discharge 

FIG.  11. — Head-discharge  characteristics. 

4.  Historical  Development. — The  centrifugal  pump  of  today 
is  a  product  of  the  last  20  years,  though  its  origin  is  of  compara- 
tively early  date.  Like  numerous  other  inventions,  the  centrifu- 
gal pump  had  many  pioneers  in  its  development  so  that  it  is 
difficult  to  justly  assign  the  credit  to  any  single  man  for  certain 
particular  features. 

It  is  said  that  Johann  Jordan  designed  a  crude  centrifugal 
pump  in  1680,  while  Papin  built  one  in  1703.  Euler  discussed 
their  theory  in  1754.  -But  these  early  pumps  were  merely 
regarded  as  curiosities.  The  first  practical  centrifugal  pump, 


10 


CENTRIFUGAL  PUMPS 


called  the  Massachusetts  pump,  was  built  in  the  United  States 
in  1818.  (See  Fig.  12.)  In  1830  a  pump  having  a  fairly  good 
efficiency  was  built  by  McCarty  at  the  dock  yards  of  New  York. 
About  1846  centrifugal  pumps  began  to  be  manufactured  in 
England  by  Appold,  Thompson,  and  Gwynne.  Appold  improved 
the  pump  by  the  addition  of  curved  vanes  in  1849.  The  addition 
of  diffusion  vanes  so  as  to  produce  the  turbine  pump  is  credited 
by  some  to  Os^orne  Reynolds  who  designed  such  a  pump  in  1875. 
This  pump  was  not  built  until  1887  and  their  commercial  manu- 
facture was  taken  up  by  Mather  and  Platt  in  1893.  By  others 


FIG.  12. — The  crude  Massachu- 
setts pump. 


FIG.   13. — The  open  type  of  im- 
peller with  curved  blades. 


the  first  turbine  pump  of  good  design  is  said  to  have  been  pro- 
duced by  Sulzer,  the  Swiss  engineer,  in  1896.  About  the  same 
time  turbine  pumps  were  built  by  Byron  Jackson,  of  San  Fran- 
cisco, and  others. 

The  placing  of  centrifugal  pump  impellers  in  series  so  as  to 
produce  the  multi-stage  pump  was  first  done  by  W.  H.  Johnson 
in  America  in  1846.  He  built  a  3-stage  pump,  but  it  appears 
to  have  been  of  little  commercial  importance.  Sulzer  is  generally 
given  the  credit  for  being  the  first  to  manufacture  multi-stage 
pumps  of  any  importance.  In  1894  he  built  a  3-stage  pump  with- 
out diffusion  vanes,  and  in  1896  he  constructed  a  4-stage  turbine 
pump.  The  latter  had  a  capacity  of  5,000  G.P.M.  under  a  head 
of  460  ft.1 

1  For  details  of  the  historical  development  see  "Evolution  of  the  Turbine 
Pump,"  Proc.  Inst.  of  Mech.  Eng.,  1912,  page  7;  W.  O.  Webber  in  Trans. 
Amer.  Soc.  of  Mech.  Eng.,  1905,  page  764;  Greene,  "Pumping  Machinery," 
page  43. 


INTRODUCTION  11 

Although  the  centrifugal  pump  has  been  in  existence  for  a  con- 
siderable period,  it  is  only  within  the  last  few  years  that  it  has 
been  widely  used  or  rapidly  improved.  The  reason  for  this  is 
that  the  centrifugal  pump  is  a  relatively  high-speed  machine 
and  until  recent  years  there  was  no  form  of  motive  power  well 
suited  to  it.  In  the  days  of  the  slow-speed  steam  engine  the 
reciprocating  pump  was  better  adapted  to  the  conditions.  But 
with  the  introduction  of  the  steam  turbine  and  the  electric  motor 
the  conditions  were  reversed.  For  such  sources  of  motive  power 
the  reciprocating  pump  is  not  as  well  adapted  as  the  centrifugal 
pump. 

5.  Conditions  of  Use  .^-Centrifugal  pumps  are  used  under  a 
wide  range  of  conditions.  They  may  lift  water  from  a  few  feet 
up  to  several  thousand.  The  Southwark  Foundry  and  Machine 
Co.  of  Philadelphia  has  built  a  small  capacity  pump  (500  G.P.M.) 
to  deliver  water  against  a  head  of  2,070  ft.  Sulzer  has  built  a 
number  of  centrifugal  pumps  for  mine  drainage  to  work  against 
heads  of  2,000  ft.  or  more.  What  is  probably  the  largest  capacity 
mine  pump  delivers  2,500  G.P.M.  against  a  head  of  2,000  ft. 
when  running  at  1,450  r.p.m.  It  is  a  7-stage  turbine  pump  driven 
by  a  1,900-h.p.  motor. 

The  largest  rate  of  discharge  of  a  single  centrifugal  pump  has 
run  as  high  as  300  cu.  ft.  per  sec.  (134,500  G.P.M.,  or  194,000,000 
gal.  per  24  hr.).  The  I.  P.  Morris  Co.  is  building  four  such  units 
for  the  Utah  Power  and  Light  Co.  to  operate  against  a  head  of 
16  ft.  when  running  at  77.5  r.p.mJuyA  photograph  of  one  of  the 
impellers  is  shown  in  Fig.  21  and  a  sectional  elevation  of  the  pump 
may  be  seen  in  Fig.  14.  It  will  be  noted  that  the  casing  and 
suction  tube  are  formed  in  concrete,  the  casing  being  of  the  volute 
type,  this  construction  being  similar  to  that  of  recent  vertical 
shaft,  single  runner  turbine  units.  The  vanes  surrounding  the 
impeller  are  really  not  diffusion  vanes  as  they  are  drawn  to  con- 
form to  the  free  path  of  the  water.  They  are  cast  solid  with  the 
foundation  ring,  which  supports  the  pump  head  cover  and  forms 
the  top  of  the  suction  tube,  and  are  designed  to  carry  the  weight 
of  the  concrete  floor  above  the  pumps  and  the  weight  of  the 
equipment.  The  steady  bearing  is  of  the  lignum  vitse  type, 
located  immediately  above  the  impeller.  This  bearing  is  lubri- 
cated by  water  only,  thus  adding  to  the  cleanliness  of  operation^) 
Another  large  capacity  pump  built  by  the  I.  P.  Morris  Co.  for 
'drainage  at  New  Orleans  delivers  294  cu.  ft.  per  sec.  under  a 


12 


CENTRIFUGAL  PUMPS 


head  of  11  ft.,  including  friction  in  short  suction  and  discharge 
pipes,  the  efficiency  under  these  conditions  being  77.5  per  cent. 
Under  a  head  of  10  ft.  the  discharge  was  320  cu.  ft.  per  sec.  with 
an  efficiency  of  74.0  per  cent.  The  diameter  of  the  discharge  is 
72  in.,  that  of  the  impeller  being  9  ft.  4  in.  It  is  driven  by  a 
500-h.p.  motor.  / 


FIG.   14. — Sections  of  a  large  centrifugal  pump.     Capacity  135,000  G.P.M., 
h  =  16  ft.,  N  =  77.5  r.p.m.     (/.  P.  Morris  Co.) 


A  large  capacity  pump  built  by  the  Southwark  Foundry  and 
Machine  Co.  is  shown  in  Fig.  15.  The  diameter  of  the  discharge 
is  76  in.  and  that  of  the  impeller  70  in.  The  normal  capacity  is 
130,000  O.P.M.  against  a  head  of  7  ft.  at  87  r.p.m.  This  pump 
delivered  168,000  G.P.M.  under  a  head  of  1.0  ft.  at  50  r.p.m.  and 
90,000  G.P.M.  under  a  head  of  13  ft.  at  115  r.p.m.  The  duty  is 
expected  "to  be  95,000,000  ft.  Ib.  per  1,000  Ib.  of  steam. 

The  largest  steam  turbine  driven  centrifugal  pump  has  been 
built  by  the  De  Laval  Steam  Turbine  Co.  It  is  shown  in  Fig. 
107,  page  166.  The  discharge  is  159  cu.  ft.  per  sec.  (71,260 
G.P.M.,  or  102,610,000  gal.  per  24  hr.)  against  a  head  of  58.7  ft, 
at  345  r.p.m.  This  is  equivalent  to  1,057  w.h.p.  The  duty, 
including  auxiliaries,  is  120,500,000  ft.  Ib.  per  1,000  Ib.  of  dry 


INTRODUCTION 


13 


steam  at  150  Ib.  gage.     The  size  of  the  discharge  is  48  in.,  the 
pump  alone  being  11  ft.  lengthwise  of  the  shaft  and  10  ft.  high.1 
/The  greatest  horse-power  of  any  type  of  centrifugal  pump  is 


FIG.  15. — Large  76-in.  centrifugal  pump. 
Machine  Co.) 


(Southwark  Foundry  and 


probably  that  of  a  pump  recently  installed  by  Sulzer  Bros,  in 
Italy.  A  single-stage  pump  running  at  1,002  r.p.m.  'delivers 
32,530  G.P.M.  at  a  head  of  498.6  ft.  with  an  efficiency  of  81.0 

1  Power,  Vol.  40,  page  644,  Nov.  3,  1914. 


14  CENTRIFUGAL  PUMP 8 

per  cent.  The  water  horse-power  is  3,590  and  the  brake  horse- 
power 4,430.  It  is  driven  by  an  electric  motor.1  For  the  vast 
majority  of  pumps  the  horse-power  is  less  than  500  and  rarely 
does  it  go  over  1,000.  The  pump  noted  above  is  remarkable 
also  for  the  high  head  per  stage  and  its  good  efficiency. 

The  diameters  of  the  discharge  pipe  connections  may  range 
from  an  inch  or  less  up  to  76  in.  Probably  the  largest  centrifugal 
pump  in  point  of  size  was  one  built  by  Prof.  James  Thompson  of 
England  for  lifting  water  to  a  height  of  4  ft.  The  diameter  of 
the  impeller  was  16  ft.  and  that  of  the  whirlpool  chamber  was 
32ft.  £/ 

For  large  pumps  under  low  heads  speeds  as  low  as  30  r.p.m. 
may  be  met  with.  High  rotative  speeds  are  naturally  found  only 
with  impellers  of  small  diameters.  Speeds  up  to  3,000  r.p.m. 
are  common.  As  illustrations  of  some  moderately  high  speeds 
the  following  may  be  mentioned:  A  2-stage  De  Laval  pump  de- 
livering 275  G.P.M.  under  a  head  of  350  ft.  at  3,000  r.p.m.,  a 
5-stage  De  Laval  pump  delivering  500  G.P.M.  under  a  head  of 
1,450  ft.  at  3,000  r.p.m.,  and  a  pump  of  German  make  with  an 
impeller  7  in.  in  diameter  delivering  900  G.P.M.  under  a  head  of 
120  ft.  at  3,300  r.p.m.  The  highest  rotative  speed  employed  is 
20,000  r.p.m.  This  was  with  a  single-stage  De  Laval  volute 
pump  with  an  impeller  2.84  in.  in  diameter.  The  pump  delivered 
250  G.P.M.  against  a  head  of  700  ft.  with  an  efficiency  of  60.0 
per  cent.,  which  was  very  good.  The  highest  peripheral  speed 
used  was  with  a  single-stage  Rateau  pump  having  an  impeller 
3.15  in.  in  diameter.  Running  at  18,000  r.p.m.  it  delivered  189 
G.P.M.  against  a  head  of  863  ft.  with  an  efficiency  of  60.0  per 
cent.  also.  This  pump  developed  a  head  as  high  as  995  ft.  with 
a  discharge  of  82  G.P.M. 

yy  Centrifugal  pumps  have  been  built  with  as  many  as  12  stages. 
In  some  instances  these  are  all  in  one  single  case,  but  for  such  a 
large  number  it  is  more  usual  to  divide  them  up  between  two 
pumps  in  series.  These  two  pumps  are  usually  placed  on  the 
opposite  sides  of  the  driver  and  reversed  so  that  the  end  thrust 
of  one  will  balance  that  of  the  other.  The  objection  to  so  many 
stages  in  a  single  case  is  that  it  necessitates  a  very  long  shaft, 
which  will  be  subject  to  vibration.  It  is  customary  to  limit  the 
head  per  stage  to  a  value  of  from  100  to  200  ft.,  but  this  has  been 
greatly  exceeded  in  a  few  cases  mentioned  above. 

1  Power,  Vol.  40,  page  413,  Sept.  22,  1914. 


INTRODUCTION 


15 


6.  Pump  Size. — By  the  size  or  number  of  a  centrifugal  pump 
is  meant  the  diameter  of  the  discharge  pipe  connection  expressed 
in  inches.  (This  is  unlike  the  practice  with  water  turbines  which 
are  rated  according  to  the  diameter  of  the  runner.)  Since  the 
design  is  usually  such  that  the  velocity  of  the  water  at  this  place 
does  not  differ  widely  from  10  ft.  per  sec.,  it  may  be  seen  that  this 
size  gives  an  index  of  "the  capacity  of  the  pump.  This  may  be 
seen  to  be  true  by  an  inspection  of  Fig.  16.  A  few  values  may 
also  be  cited  which  are  beyond  the  scale  of  the  curve.  A  54-in. 


12 


Rate  of  Discharge  in  Cu.  Pit.  per  Sec. 
16          20          24          28          32          36  • 


52 


34 


2  26 

f  « 

I  20 

0  18 
S1  16 

1  14 

?5 


0          2,000       4,000       6,000       8,000      10,000     12,000      14,000     16,000     18,000      20,000     22,000     24,000 
Rate  oLDischarge  in  Gal.  per  Min. 

FIG.  16. — Relation  between  pump  capacity  and  the  size  of  the  discharge 

flange. 

pump  was  rated  at  75,000  G. P.M.  corresponding  to  a  velocity  of 
10.5  ft.  per  sec.  Two  72-in.  pumps  had  discharges  of  125,500 
and  132,000  G.P.M.  corresponding  to  velocities  of  9.9  and  10.4 
ft.  per  sec.  respectively.  Since  the  velocity  of  flow  at  discharge 
may  really  vary  from  5  to  15  ft.  per  sec.,  this  rating  cannot  be 
relied  upon  exactly.  Nevertheless  it  is  a  very  convenient  "rule 
of  thumb."  As  will  be  shown  later,  the  capacity  of  any  given 
pump  depends  upon  the  speed  at  which  it  is  run. 

7.  Rated  Head  and  Discharge. — As  may  be  seen  in  Fig.  11, 
the  rate  of  discharge  of  a  centrifugal  pump  running  at  a  given 
speed  will  vary  according  to  the  head  against  which  the  pump 
works.  The  rated  head  and  discharge  for  the  pump  will  be  the 
values  for  which  the  efficiency  is  a  maximum.  This  value  of 
the  discharge  is  often  designated  as  the  normal  discharge.  These 
values  will  be  different  for  different  speeds. 


CHAPTER  II 
DESCRIPTION 

8.  The  Impeller. — Impellers  are  either  of  the  open  or  the  en- 
closed type.  The  former  is  shown  in  Fig.  13,  page  10.  It  may 
be  seen  that  this  was  a  natural  evolution  of  the  impeller  of  the 
primitive  pumps  such  as  that  in  Fig.  12.  In  1849  it  was  demon- 
strated that  curved  vanes  were  superior  to  the  straight  vanes. 
It  was  also  found  desirable  to  add  a  web  at  one  side  of  the  vanes 


r 


FIG.   17. — Single  suction  impeller. 

in  order  to  stiffen  them,  thereby  enabling  them  to  be  made  thinner. 
This  web  extends  from  the  center  to  the  outer  circumference  in 
most  cases  though  it  may  not  always  do  so.  The  impeller  was 
further  improved  by  the  addition  of  a  shroud  on  the  outside,  thus 
producing  the  enclosed  or  shrouded  impeller. 

Impellers  may  be  either  single  suction,  called  also  -side  suction, 
or  double  suction  as  shown  in  Figs.  17  and  18.  The  latter  is 
used  for  larger  discharges  than  would  be  possible  with  the  same 
diameter  of  impeller  of  the  former  type.  It  has  the  further 
advantage  that  end  thrust  is  eliminated.  The  double  suction 
impeller  may  have  two  separate  suction  pipes  or  the  water  pas- 
sages may  be  divided  within  the  case  as  in  Fig.  24. 

16 


DESCRIPTION 


17 


Impellers  are  usually  cast  in  one  piece  and  are  made  of  iron, 
brass  or  bronze.  The  last  mentioned  is  much  better  as  it  does 
not  corrode.  This  not  only  prolongs  its  life  but  enables  it  to 
retain  its  smooth  finish,  which  is  conducive  to  better  efficiency. 


Sect! 


FIG.   18. — Double  suction  impeller. 

For  very  high  speeds  it  is  sometimes  necessary  to  machine  the 
impeller  out  of  solid  steel  forgings.  In  other  cases  blades  pressed 
out  of  sheet  steel  may  be  riveted  or  cast  to  the  web.  In  the 
best  pumps  the  impeller  will  be  finished  all  over.  But  for  pur- 
poses such  as  dredging,  where  the  impeller  is  subjected  to  great 
wear,  this  is  an  unnecessary  expense.  In  some  instances  where 


FIG.  19. — Impellers  of  a  4-stage  pump.     (Henry  R.  Worthington.) 

acid  is  to  be  pumped  cast-iron  impellers  have  been  employed 
without  any  finishing.  The  skin  of  the  casting  enables  it  to 
withstand  the  acid  better.  Also,  owing  to  their  comparatively 
short  life,  it  is  desirable  to  keep  their  cost  as  low  as  possible.  It 
would  be  better,  if  possible,  to  make  them  of  some  acid-proof 
metal. 
2 


18 


CENTRIFUGAL  PUMPS 


In  some  instances  impellers  have  half  vanes  inserted  in  order  to 
improve  the  guidance  of  the  water  and  prevent  instability  of  flow 
due  to  too  greatly  diverging  passages.  Such  are  illustrated  in  the 
section  drawing  in  Fig.  64. 


FIG.  20. — Impeller  for  a  42-inch  centrifugal  pump.  Diameter  of  impeller 
=  144  inches,  capacity  =  44,800  G.P.M.,  h  =  35  ft.,  N  =  100  r.p.m.  (R. 
D.  Wood  and  Co.) 

The  ratio  of  the  diameter  of  the  impeller  to  the  width  at  exit, 
D/B  in  Figs.  17  and  18,  is  often  called  the  type  of  the  impeller. 
It  may  readily  be  seen  that  a  given  discharge  area  may  be  secured 
with  either  a  large  diameter  and  a  narrow  width  or  a  small  diame- 
ter and  a  large  width.  It  will  be  shown  later  that  this  materially 


DESCRIPTION 


19 


FIG.  21. — Single  suction  impeller.  Diameter  =110  inches,  weight  = 
22,500  Ib.  Capacity  134,500  G.P.M.,  h  =  16  ft.,  N  =  77.5  r.p.m.  (7.  P. 
Morris  Co.) 


FIG.  22. — Double  suction  impeller.     (De  Laval  Steam  Turbine  Co.) 


20 


CENTRIFUGAL  PUMPS 


FIG.  23. — Double    suction    impeller    in    split    case.     (Platt    Iron    Works.) 


FIG.  24. — Double  suction  volute  pump.     (Alberger  Pump  and  Condenser  Co.) 


DESCRIPTION     .  21 

affects  the  efficiency  of  the  pump.     Values  of  this  ratio  may  range 
from  2  to  70,  though  these  are  not  necessarily  absolute  limits. 

9.  Diffuser. — The  diffusion  vanes  are  usually  of  bronze  or 
steel.  It  is  very  desirable  that  they  be  finished  smooth  in  order 
to  minimize  the  losses,  hence  they  are  left  open  on  one  side  so 
that  they  can  be  machined.  A  cover  plate  is  then  bolted  on  to 
form  the  complete  diffuser. 


FIG.  25. — Diffusion    vanes  for  turbine  pump.     (Henry  R.   Worthington.) 

If  the  case  is  circular  as  shown  in  Fig.  2,  the  vanes  are  so  con- 
structed as  to  discharge  the  water  nearly  radially.  Such  a 
direction  of  flow  is  more  desirable  as  may  be  seen  by  noting  the 
stream  lines  shown  in  the  figure. 

If  the  case  is  spiral,  as  in  Fig.  3,  the  diffuser  is  so  designed  as 
to  send  the  water  into  the  case  with  a  velocity  having  a  tangential 
component,  as  this  is  then  more  desirable.  The  velocity  of 
discharge  from  the  diffuser  may  be  high  for  there  is  still  opportu- 
nity to  further  transform  velocity  into  pressure,  the  same  as  in 
the  plain  volute  pump  without  the  diffusion  vanes.  For  this  rea- 


22 


CENTRIFUGAL  PUMPS 


son  the  velocity  of  flow  in  the  case  itself  may  be  permitted  to  be 
much  higher  in  the  spiral  case  than  in  the  circular  case. 

10.  Clearance  Rings. — In  order  to  reduce  the  leakage  of  water 
from  the  discharge  to  the  suction  sides  of  the  impeller,  close-run- 
ning fits  are  employed.  These  are  called  clearance  rings  or  wear- 
ing rings.  As  wear  will  cause  these  spaces  to  enlarge,  the  rings 
are  generally  made  separate  from  the  impeller  and  case  so  that 
they  may  be  renewed. 

It  is  desirable  that  these  rings  be  of  as  small  a  diameter  as 
possible  in  order  to  reduce  the  leakage  area  to  a  minimum. 


D  E 

FIG.  26. — Various  forms  of  labyrinth  rings. 

Therefore  the  rings  are  placed  as  near  to  the  "eye"  of  the  im- 
peller as  possible.  Sometimes  both  an  outer  and  an  inner  set 
are  employed. 

In  order  to  impede  the  flow  of  the  water  and  at  the  same  time 
permit  of  large  clearances,  labyrinth  rings  (Fig.  26)  are  employed. 
It  is  of  advantage  not  to  have  the  clearances  too  small,  otherwise 
vibration  of  the  shaft  or  end  play  would  bring  the  surfaces  into 
contact. 

The  rings  are  usually  made  of  bronze. 

11.  Stuffing  Boxes. — Water  is  prevented  from  leaking  out  at 
the  high-pressure  end  of  the  shaft,  and  air  from  leaking  in  at  the 
suction  end  by  means  of  stuffing  boxes.  (See  Fig.  9.)  The  pack- 
ing on  the  suction  end  is  usually  divided  into  two  parts  by  means 
of  a  gland  cage,  which  leaves  an  open  space.  Water  is  admitted 
into  this  space  so  that  it  may  be  drawn  into  the  pump  rather  than 
air.  Thus  the  suction  is  prevented  from  being  destroyed. 


DESCRIPTION 


23 


In  a  multi-stage  pump  water  is  prevented  from  leaking  along 
the  shaft  from  one  stage  to  another  merely  by  means  of  a  long 
close- running  fit.  (See  Fig.  32.) 

12.  The  Case. — Cases  are  usually  made  of  cast  iron.  For 
high  pressures  they  may  be  made  of  cast  steel.  In  some  instances 
cast-iron  cases  may  be  lined  with  steel  in  order  to  enable  them  to 
withstand  the  excessive  wear  to  which  they  are  subjected  in  such 
services  as  dredging. 

As  has  already  been  stated,  cases  are  divided  into  the  circular 
and  the  spiral  or  volute  types.  The  latter  is  often  called  a  scroll 


FIG.  27.— Split  case  volute  pump.     (De  Laval  Steam  Turbine  Co.} 

case.  But  a  more  important  distinction  is  as  to  how  they  may 
be  opened  up  so  as  to  get  at  the  interior  of  the  pump.  One  type 
is  the  horizontally  split  case  such  as  is  shown  in  Fig.  27.  The 
other  is  t  he-side  plate  type  shown  in  Fig.  28  and  Fig.  9,  page  7. 
This  latter  is  sometimes  called  the  vertically  split  case,  but  ob- 
viously the  distinctions  as  to  horizontal  and  vertical  are  only 
appropriate  in  the  case  of  the  horizontal  shaft  pump. 

In  general  the  split  case  makes  the  pump  easier  to  inspect,  take 
apart  or  repair.  Also  it  is  never  necessary  to  disconnect  the  pip- 
ing when  it  is  desired  to  open  up  the  pump.  The  side-plate  type 
is  apt  to  be  a  more  economical  form  of  construction  but  it  is  more 
difficult  to  get  at  the  interior,  especially  in  the  case  of  multi-stage 


24 


CENTRIFUGAL  PUMPS 


pumps.  Also  with  this  type  it  is  usually  necessary  to  disconnect 
at  least  the  suction  piping.  But  it  is  possible  to  have  the  piping 
connected  to  the  case  proper  so  that  the  plates  can  be  readily 
removed. 

With  multi-stage  pumps  of  the  side  plate  type  we  may  have 
either  the  sectional  or  the  solid  construction.     The  former  con- 


FIG.  28.— Side  plate  casing.     (R.  D.  Wood  and  Co.) 

sists  of  a  number  of  independent  sections  bolted  together  as  in 
Fig.  33  and  Fig.  5,  page  4.  The  solid  casing  is  shown  in  Fig.  63. 
As  is  seen,  it  consists  of  a  shell  cast  in  one  piece  and  long  enough 
to  contain  all  the  stages.  The  impellers  and  other  parts  are  intro- 
duced from  the  end.  The  former  has  advantages  in  manufacture 
as  any  number  of  stages  can  be  had  with  a  single  casing  pattern. 


DESCRIPTION 


25 


However,  it  is  necessary  to  use  great  care  in  lining  up  all  the  differ- 
ent sections.  It  is  thought  that  the  latter  form  might  be  more 
difficult  to  take  apart,  especially  if  some  of  the  parts  should  rust 
fast  together.  Also  it  is  difficult  to  assemble  it  properly,  if  there 
are  many  stages. 

With  the  multi-stage  pump  the  water  is  led  from  the  discharge 
chamber  of  one  impeller  to  the  suction  of  the  next  impeller  by 


FIG.  29. — Volute  centrifugal  pump.     (Henry  R.  Worthington.) 

means  of  the  reversing  channels,  shown  in  Figs.  32  and  33. 
These  channels  usually  have  directing  vanes  in  them  to  guide  the 
water  and  prevent  its  rotating.  The  chamber  surrounding  each 
stage,  except  the  last,  should  be  circular,  since  equal  quantities  of 
water  flow  from  it  into  the  reversing  channels  all  around  the  cir- 
cumference. But  with  the  last  stage  the  case  may  be  either 
spiral  or  circular,  just  as  in  the  case  of  a  single-stage  pump. 

The  arrangement  of  impellers  in  the  multi-stage  pumps  shown 
in  Figs.  30,  31,  32  and  33  is  called,  from  the  originator,  the  Jaeger 
type.  It  is  the  simplest  form  of  construction  and  has  beeiTthe 
most  widely  used.  Another  very  compact  type  is  the  Kugel- 
Gelpe  construction  shown  in  Fig.  34.  The  latter  is  made  in  this 
country  by  the  Allis-Chalmers 


26 


CENTRIFUGAL  PUMPS 


FIG.  30. — Three-stage  centrifugal  pump  without  diffusion  vanes. 
(Platt  Iron  Works.) 


FIG.  31. — Two-stage  centrifugal  pump  with  diffusion  vanes. 
(Platt   Iron  Works.) 


DESCRIPTION 


27 


| 


I 

0) 

S 


28 


CENTRIFUGAL  PUMPS 


DESCRIPTION 


29 


I 


30 


CENTRIFUGAL  PUMPS 


13.  Balancing. — With  a  centrifugal  pump  impeller,  such  as 
shown  in  Fig.  35,  there  will  be  found  an  end  thrust  which  must 
be  provided  for.  This  thrust  may  be  taken  up  entirely  by  a 
thrust  bearing.  Or  the  thrust  can  be  taken  care  of  by  what  is 
called  hydraulic  balancing.  The  latter  met  hod  Jin  volves  the 
circulation  of  a  small  quantity  of  water,  which  may  be  allowed 
to  escape  outside  or  which  is  more  usually  "  short  circuited" 
so  that  it  returns  to  the  suction  side  of  the  impeller.  But  the 
additional  work  due  to  pumping  this  leakage  water  will  usually 
be  far  less  than  that  necessary  to  overcome  the  friction  of  a 
thrust  bearing. 

With  some  methods  only  partial  balance  is  attained  and  in 
other  cases  the  balancing  must  be  regulated  by  hand.  In  such 
instances  it  is  necessary  to  have  a  bearing  to 
take  care  of  the  excess  thrust.  With  other 
methods  complete  balance  is  obtained  so  that 
the  thrust  bearing  is  practically  eliminated. 
However,  even  in  these  cases,  it  is  well  to  have 
some  thrust  bearing  in  order  that  a  failure  of 
the  automatic  balancing  device  should  not 
cause  the  shut  down  of  the  pump. 

This  thrust  may  be  caused  by  two  things: 
(1)  It  is  necessary  to  change  the  momentum  of 
the  water  at  entrance  to  the  impeller  from  an 
axial  to  a  radial  direction.     This  causes  a  thrust 
upon  the  impeller  tending  to  move  it  away  from 
the  suction  side.     In  Fig.  35  it  would  tend  to 
move  the  impeller  to  the  right.     The  value  of  the  force  would 
be  (W/g)Vi* 

(2)  There  will  be  a  pressure  on  the  right-hand  side  of  the  web 
equal  in  intensity  to  that  existing  at  the  point  of  exit  from  the 
impeller.  This  pressure  may  be  considered  as  acting  upon  two 
areas,  one  the  portion  opposite  to  the  "eye"  and  the  other  the 
annular  ring  corresponding  to  the  shroud.  It  is  evident  that  upon 
the  inner  portion  there  will  be  a  resultant  thrust  equal  to  the 
area  of  the  "eye"  times  the  difference  between  the  pressures  at 
exit  and  entrance  to  the  impeller.  Since  the  water  on  the  left- 
hand  side  of  the  shroud  continually  escapes  through  the  clearance 
rings,  it  is  possible  that  the  average  intensity  of  pressure  there 
may  be  less  than  that  on  the  corresponding  portion  of  the  web. 
*  For  notation,  see  page  44. 


FIG.  35. 


DESCRIPTION 


31 


This  will  certainly  be  so  in  case  the  impeller  is  equipped  with 
both  an  outer  and  an  inner  set  of  rings.  Thus  this  thrust,  what- 
ever it  be  in  value,  must  be  added  to  the  former.  The  total 
thrust  from  these  sources  acts  toward  the  suction  side,  that  is 
toward  the  left  in  Fig.  35. 

If  it  is  an  open  impeller,  then  we  do  not  have  the  counter- 
balancing force  on  the  shroud.  The  pressure  within  the  impeller 
will  be  less  than  that  at  a  similar  point  in  the  clearance  spaces. 


FIG.  36. — Vertical  shaft  pump  with  suction  above. 

Condenser  Co.) 


(Alberger  Pump  and 


The  result  will  be  a  greater  amount  of  thrust  toward  tne  suc- 
tion side  than  would  be  the  case  with  a  shrouded  impeller. 

It  is  seen  that  (1)  and  (2)  oppose  each  other.  However,  the 
latter  is,  in  general,  greater  than  the  former  so  that  the  total 
resultant  thrust  is  toward  the  suction  end.  For  this  reason 
vertical  shaft  pumps  often  have  the  suction  on  the  upper  side 
as  in  Fig.  36,  so  that  the  resultant  thrust  may  aid  in  supporting 
the  weight  of  the  rotating  parts.  However,  as  a  good  thrust 
bearing  is  required  in  any  vertical  shaft  pump,  it  is  not  necessary 


32 


CENTRIFUGAL  PUMPS 


to  strive  for  perfect  balance.  As  will  be  seen  later,  it  may  be 
possible  to  practically  eliminate  (2).  In  such  cases  we  could 
have  the  suction  on  the  lower  side  as  in  Fig.  102,  page  162.  In  this 
case,  also,  the  thrust  due  to  (1)  alone  aids  in  supporting  the  weight, 
but  it  is  probably  somewhat  less  in  value  than  in  the  former  case. 
B&JLeau  endeavored  to  solve  the  problem  for  the  horizontal 
pump  by  making  (1)  and  (2)  equal.  To  do  this  an  annular  ring 
was  omitted  from  the  outer  part  of  the  web,  while  the  shroud 
still  extended  to  the  tips  of  the  blades.  Thus  (2)  would  be  de- 
creased, since  the  area  would  be  decreased.  But  also  the  force 


FIG.  37.— Thrust  bearing.     (Henry  R.  Worthington.} 


on  the  left  of  the  shroud  (Fig.  35)  opposite  the  portion  of  the  web 
that  was  removed  would  not  be  balanced  by  an  equal  and  opposite 
force,  since  the  pressure  within  the  impeller  would  be  less  than 
that  in  the  clearance  space.  Thus  there  would  be  a  force  to  be 
added  to  that  of  (1).  The  defect  of  this  arrangement  is  that 
accurate  balancing  can  be  determined  only  by  trial,  since  the 
forces  cannot  be  calculated  with  sufficient  exactness  to  enable  one 
to  know  how  much  the  web  should  be  cut  back.  Also,  since  both 
(1)  and  (2)  vary  with  the  discharge,  perfect  balance  is  possible 
for  only  one  given  rate  of  discharge.  It  may  further  be  shown 
that  leaving  a  portion  of  the  impeller  open  induces  greater  hy- 
draulic and  disk  friction  losses  than  would  be  the  case  with  a 
completely  enclosed  impeller. 


DESCRIPTION  33 

It  is  possible  to  practically  eliminate  (2)  by  inserting  a  clear- 
ance ring  on  the  back  of  the  web  exactly  similar  to  that  on  the 
shroud.  Holes  are  then  made  through  the  web  near  the  hub  so 
that  the  leakage  may  return  to  the  suction  and  prevent  the  pres- 
sure on  the  back  from  building  up.  (See  Figs.  9,  21,  32.)  There 
is  then  left  only  the  effect  of  (1). 

In  order  to  eliminate  (1)  as  well,  double  suction  impellers  are 
often  used,  especially  for  single-stage  pumps.  They  are  also  used 
for  multi-stage  pumps,  but,  as  may  readily  be  seen,  such  types 
of  pumps  are  longer,  more  costly,  and  more  difficult  of  design. 
But  aside  fro^n  eliminating  the  end  thrust,  they  have  the  marked 
advantage  that  a  smaller  diameter  of  impeller  is  possible  than 
could  be  had  with  a  single  suction  impeller  of  the  same  capacity. 
That  is,  it  is  possible  to  secure  a  lower  value  of  the  ratio  D/B 
(Fig.  18) .  This  will  be  shown  later  to  be  desirable  from  the  stand- 


FIG.  38. — Double  pumping  unit  with  rope  drive.     Capacity  of  each  pump  = 
2,000  G.P.M.,  h  =  415  ft.,  N  =  450  r.p.m.     (Morris  Machine  Works.) 

point  of  efficiency  and  it  will  also  permit  of  a  higher  speed  of  rota- 
tion, which  is  often  a  point  that  is  striven  for.  Though  this  last 
type  of  multi-stage  pump  is  not  yet  common,  it  is  increasing 
in  popularity.  Anything  which  tends  to  cause  different  amounts 
of  water  to  enter  the  two  sides  of  the  impeller  or  unequal  leakage 
past  the  two  clearance  rings  would  disturb  the  equilibrium  and 
produce  an  end  thrust.  This  must  be  prevented,  as  shown  further 
over. 

The  thrust  may  also  be  provided  for  by  dividing  the  water 
between  a  pair  of  pumps  as  shown  in  Fig.  38.  These  are  so  ar- 
ranged that  the  thrust  of  one  is  opposite  in  direction  to  that  of  the 
other.  Often  a  multistage  pump  may  be  divided  up  into  two 


34 


CENTRIFUGAL  PUMPS 


parts  on  opposite  sides  of  the  driver  and  the  water  passed  from 
one  to  the  other  in  series.  Not  only  does  this  arrangement  elimi- 
nate the  thrust  but  it  also  avoids  an  extra  long  shaft  between 
bearings  with  its  attendant  vibration  troubles. 


FIG.  39.  (a). — Four-stage  pump  with  opposed  impellers. 
(Morris  Machine  Works.) 


FIG.  39.  (6). — Multi-stage  pump  with  opposed  impellers. 

(Morris  Machine  Works.) 

In  the  construction  shown  in  Fig.  39  (a)  the  suction  intake  is 
in  the  center  of  the  pump.  Numbering  the  impellers  from  left  to 
right,  the  water  flows  through  impellers  3,  4,  2  and  1.  The  water 
is  led  from  the  discharge  chamber  of  4  to  the  suction  chamber  of  2 


DESCRIPTION  35 

by  a  channel  contained  in  the  raised  part  on  the  right-hand  end  of 
the  cover  of  the  pump  in  Fig.  39(6).  This  arrangement  not  only 
provides  hydraulic  balance,  but  eliminates  the  suction  stuffing 
box.  Other  similar  arrangements  have  been  made  which  bring 
the  high  pressure  sides  together  in  the  center,  thereby  eliminating 
the  other  stuffing  box  instead  of  the  suction  gland. 

In  Fig.  40  we  see  a  2-stage  pump  with  the  impellers  opposed. 
The  discharge  of  one  is  led  around  to  the  other  side  of  the  second. 
If  this  had  been  a  pump  with  diffusion  vanes,  and  more  than  two 
stages,  these  passages  would  have  had  to  go  through  the  diffuser, 
using  for  this  purpose  the  open  spaces  which  may  be  seen  in  Fig. 
25.  (However  in  this  figure  these  openings  are  merely  left  to  save 


FIG.  40. — Two-stage  pump  with  opposed  impellers.     (R.  D.  Wood  and  Co.) 

metal.)  The  pump  with  the  impellers  back  to  back  is  known  as 
the  gi]j7.pr  typp.  Owing  to  the  somewhat  complicated  passages, 
the  fact  that  there  must  always  be  an  even  number  of  stages  and 
that  both  right-  and  left-handed  impellers  must  be  built,  this 
type  is  but  little  used  at  present. 

All  of  the  above  means  of  eliminating  thrust  are  imperfect. 
In  some  of  them  the  thrust  is  not  eliminated  entirely,  it  is  merely 
minimized.  In  others  the  thrust  is  eliminated  for  one  condition 
of  operation  only.  With  the  third  group  perfect  balance  is  only 
possible  with  perfect  construction.  Inaccuracies  in  workmanship, 
unequal  wear,  or  other  similar  causes  permit  a  thrust  to  be  ex- 
erted, even  with  double  suction  impellers. 


36  CENTRIFUGAL  PUMPS 

Perfect  hydraulic  balancing  can  be  secured  only  by  balancing 
pistons  or  similar  devices.  The  simplest  case  to  consider  is  that 
of  a  double  suction  impeller  such  as  that  in  Fig.  24,  page  20. 
Here  we  find  a  clearance  ring  with  both  axial  and  radial  fissures. 
If  the  impeller  moves  toward  the  right,  for  instance,  the  axial 
fissures  are  left  unchanged  in  value  but  the  radial  fissure  on  the 
left  opens  up  while  that  on  the  right  closes.  The  result  is  that 
more  water  escapes  from  the  left-hand  clearance  space  than  from 
the  right-hand  clearance  space.  This  decreases  the  pressure 
on  the  left,  while  that  on  the  right  increases,  thus  providing  a  force 
to  bring  the  impeller  back  to  the  center.  The  same  device  may 
be  applied  to  the  single  suction  impeller  as  in  Fig.  9,  page  7. 

It  is  seen  that  such  devices  require  a  certain  amount  of  end  play 
in  order  to  be  effective.  If  it  is  desired  to  also  use  a  thrust  bearing 
for  emergencies,  it  is  necessary  that  it  should  not  act  until 
after  a  certain  movement  has  taken  place.  This  may  be  accom- 
plished by  a  marine  thrust  bearing  with  collars  rotating  within  a 
bushing  which  is  held  from  rotating  by  a  feather  key.  This  key 
permits  it  to  slide  endwise  until  it  strikes  a  stop,  after  which  it 
acts.1 

In  Fig.  32  each  impeller  is  balanced  in  itself.  In  Fig.  41  all  the 
balancing  is  done  by  one  balancing  chamber  at  the  right-hand  end 
of  the  last  stage.  The  other  impellers  have  no  clearance  rings 
on  their  webs  and  no  holes  through  which  the  water  could  return 
to  the  suction.  But  the  last  impeller  is  provided  with  clearance 
rings  on  the  web  through  which  water  may  leak  to  the  balancing 
chamber.  The  leakage  from  this  space  takes  place  between  two 
collars,  one  fixed  to  the  case  while  the  other  is  attached  to  the 
shaft.  If  the  shaft  moves  toward  the  right,  water  is  admitted 
more  freely  through  the  labyrinth  rings,  while  the  escape  is  cut  off. 
Thus  the  pressure  builds  up  and  returns  the  shaft  to  the  normal 
position.  On  the  other  hand,  if  the  shaft  moves  to  the  left,  the 
water  escapes  more  freely  from  this  space  while  admission  to  it 
through  the  labyrinths  is  restricted.  Thus  the  pressure  drops 
and  enables  the  shaft  to  move  back  again.  This  device  is 
recommended  only  for  clear  water  as  wear  would  decrease  its 
effectiveness.  For  gritty  water,  the  arrangement  of  Fig.  32  is 
advised. 

A  special  device  attached  to  the  shaft  for  this  purpose  is  called 
a  balancing  piston  or  disk.  See  Figs.  34,  42  and  43.  They  are 

1  Loewenstein  and  Crissey,  " Centrifugal  Pumps,"  page  258. 


DESCRIPTION 


37 


38 


CENTRIFUGAL  PUMPS 


very  similar  in  principle  as  all  depend  upon  the  combination  of 
two  fissures,  the  area  of  one  remaining  unchanged  while  that  of 
the  other  varies.  The  method  of  operation  is  the  same  as  that 
described  in  the  preceding  paragraph.  If  the  shaft  in  Fig.  43(a) 
moves  to  the  left,  the  variable  fissure,  vt  closes  up.  This  allows 
the  pressure  on  the  left-hand  side  of  the  piston  to  increase, 
while  that  on  the  right-hand  side  decreases.  The  resultant 
force  on  the  piston  is  therefore  directed  toward  the  right.  On 


FIG.  42. — Multi-stage  pump  with  balancing  piston  (No.  7). 
(Allis-Chalmers  Mfg.  Co.) 

the  other  hand,  if  the  shaft  moves  to  the  right,  the  opening  of  the 
variable  fissure  permits  the  pressure  on  the  left  of  the  piston  to 
decrease  and  thus  allows  the  shaft  to  drift  back  to  its  normal 
position.  The  Sulzer  balancing  piston  may  also  have  the  vari- 
able fissure  precede  the  constant  fissure,  c,  rather  than  follow  it  as 
shown  in  this  figure. 

In  Fig.  43(6)  another  type  of  balancing  piston  is  shown.  It 
differs  from  the  other  in  that  the  variable  fissure  is  located  nearer 
the  center.  This  has  the  advantage  that  for  the  same  total  leak- 
age area  the  clearance  can  be  greater,  resulting  in  a  longer  life 
and  less  sensitiveness.  If,  with  this  type,  the  shaft  moves  to  the 
left,  the  fissure  opens  up  so  as  to  permit  the  pressure  on  the  left- 


DESCRIPTION 


39 


hand  side  of  the  piston  to  become  greater  than  that  on  the  right 
and  thus  oppose  the  movement.  The  placing  of  v  after  c  has 
certain  mechanical  advantages  as  can  be  seen.  But  it  may  be 
placed  first  as  in  the  left-hand  portion  of  Fig.  43  (c)* 

For  large  pumps  and  those  handling  gritty  water  the  form 
shown  in  Fig.  43  (c)  is  especially  desirable.  This  has  a  second 
variable  throttling  space  provided  at  (2).  When  new,  this  space 
is  open  too  much  to  be  effective.  But  as  wear  occurs  along  the 


Impeller 


Sulzer  Schwartzkopff 

FIG.  43. — Typical  hydraulic  balancing  devices. 

constant  fissure,  the  rate  of  leakage  is  too  great  to  enable  the 
thrust  to  be  balanced  by  the  pressure  on  the  left  of  the  piston  and 
the  shaft  drifts  further  toward  the  left.  But  when  it  does  so"(2) 
closes  up  and  permits  the  pressure  to  build  up,  and  also  provides 
an  increased  area  upon  which  it  may  act.  At  the  same  time  (1) 
is  left  small  enough  to  strain  out  gritty  material.1 

The  use  of  a  balancing  piston  obviates  the  need  for  a  high  pres- 
sure packing  gland.  The  water  leakage,  which  is  small,  may  be 
returned  to  the  suction  or  may  often  be  used  for  cooling  bearings. 

1  A.  V.  Mueller,  Eng.  News,  Vol.  70,  page  490. 


CHAPTER  III 
INSTALLATION  AND  OPERATION 

14.  Priming. — It  is  impossible  for  the  centrifugal  pump  to  act 
as  an  air  pump  and  lift  water  up  to  it,  as  it  can  create  only  a  slight 
vacuum.     It  is  therefore  necessary  to  prime  it  by  some  means 
at  the  start.     This  may  be  done  either  by  filling  it  with  water 
from  some  other  source  or  exhausting  the  air  and  thus  drawing 
water  up  the  suction  pipe. 

The  pump jghould  never  be  runjemgty  as  the  packings  and  cer- 
tain other  parts_often  depend  upon  water  for  their  lubrication. 

If  the  bottom  of  the  suction  pipe  is  provided  with  a  foot  valve, 
the  pump  can  be  filled  with  water  from  some  other  source.  The 
pet  cocks  on  the  top  of  the  pump  passages  should  all  be  opened  in 
order  to  let  out  the  air.  When  water  appears  from  them,  they 
may  be  closed,  the  water  shut  off ,  and  the  pump  started. 

For  many  small  pumps  a  priming  attachment  is  often  provided 
which  consists  of  a  hand  pump  by  means  of  which  the  air  may  be 
expelled.  If  this  arrangement  is  employed,  it  is  necessary  to 
have  a  tight  valve  on  the  discharge  side  of  the  pump. 

Either  water  is  delivered  to  the  case  or  air  exhausted'  from  it  by 
means  of  steam  injectors,  compressed  air,  or  other  devices  accord- 
ing to  circumstances.  It  is  necessary  with  all  of  these  to  have  a 
valve  of  some  type  on  the  discharge  side  of  the  pump.  It  is 
customary  to  have  a  foot  valve  at  the  bottom  of  the  suction  pipe 
also  but  in  some  special  cases  this  may  not  be  necessary. 

15.  Foot  Valves  and  Strainers. — It  is  very  important  to  mini- 
mize the  losses  in  the  suction  pipe.     Therefore  the  area  through 
the  foot  valve  should  be  ample  and  it  should  be  so  constructed 
that  the  flaps  swing  up  and  out  of  the  way  when  water  is  flowing. 
The  area  through  the  foot  valve  ought  to  be  about  twice  the  area 
of  the  suction  pipe. 

It  is  often  necessary  to  have  a  strainer  outside  the  foot  valve 
to  prevent  trash  and  large  objects  from  being  drawn  into  the 
pump.  The  area  through  the  strainer  should  be  at  least  twice 
the  area  of  the  suction  pipe. 

40 


INSTALLATION  AND  OPERATION  41 

16.  Suction  Lift. — A  centrifugal  pump  will  work  under  as  high 
a  suction  lift  as  any  other  type  of  pump,  but  it  is  necessary  to 
prime  it  at  starting  as  has  been  stated.  It  has  one  advantage 
over  the  reciprocating  pump,  which  is  that  the  flow  is  continuous 
rather  than  pulsating.  This  permits  of  a  higher  suction  lift 
being  employed,  since  there  are  no  inertia  forces  to  cause  the 
suction  pressure  to  fluctuate  below  the  normal  value. 

The  height  to  which  water  may  be  lifted  in  any  pump  depends 
upon  the  pressure  of  the  atmosphere  and  the  temperature  of  the 
liquid.  The  higher  the  temperature  of  the  liquid  the  lower  the 
pressure  at  which  its  conversion  into  vapor  takes  place.  It  is 
possible  to  lift  water  a  few  feet  at  a  temperature  of  150°  F.,  but 
it  is  safer  to  cause  all  hot  water  to  flow  to  the  pump  under  posi- 
tive pressure.  If  the  water  is  very  near  212°  F.  it  should  be 
under  considerable  pressure  at  the  entrance  to  the  pump.  For 
water  at  ordinary  temperatures  it  is  well  to  keep  its  absolute 
pressure  at  least  5  ft.  of  water.  Allowing  for  the  usual  friction 
losses  and  velocity  head,  this  means  that  the  maximum  suction 
lift  should  not  exceed  25  ft.  where  the  pressure  of  the  air  is  34  ft. 
At  high  elevations  the  lift  must  be  less  than  this.  While  it  is 
possible  to  lift  water  25  ft.  in  most  cases,  it  is  well  to  keep  the 
suction  lift  as  low  as  possible. 

In  order  to  prevent  air  from  being  drawn  into  the  suction  pipe 
by  means  of  a  vortex  set  up  at  the  mouth,  it  is  well  to  place  the 
entrance  of  the  pipe  at  least  3  ft.  below  the  surface  of  the  water. 
If  this  is  not  done,  the  entrance  velocity  should  be  kept  low.  It 
is  needless  to  say  that  the  entire  suction  line  should  be  made  as 
nearly  air  tight  as  possible.  The  leakage  of  air  cuts  down  the 
capacity  of  the  pump  and  may  even  destroy  the  suction  so  as  to 
cause  the  cessation  of  flow. 

A  strong  reason  for  keeping  the  absolute  pressure  of  the  water 
as  high  as  possible  is  that  all  water  holds  air  in  solution,  which 
may  be  liberated  if  the  pressure  becomes  too  low.  Gases  are 
most  readily  absorbed  by  sprays  and  are  easily  liberated  in  an 
eddy.  Thus  a  check  valve,  a  tee,  or  sudden  change  in  pipe 
diameter  in  the  suction  line  may  set  this  air  free.  This  air  is  not 
readily  reabsorbed  in  the  flow  through  the  discharge.  Water 
absorbs  oxygen  from  the  air  more  readily  than  the  nitrogen.1 

1  At  60°  F.  and  a  pressure  of  34  ft.  of  water  absolute,  water  may  hold 
in  solution  3  per  cent,  of  its  volume  in  oxygen  and  1.5  per  cent,  of  nitrogen 
Under  half  this  pressure  it  may  hold  half  of  the  above. 


42 


CENTRIFUGAL  PUMPS 


Thus  when  this  mixture  is  liberated  either  by  too  low  a  pressure 
or  by  an  eddy,  its  corrosive  action  is  greater  than  that  of  pure  air. 
Aside  from  the  question  of  the  liberation  of  air,  if  the  pressure 
becomes  too  low,  water  vapor  is  formed.  Bearing  in  mind  the 
fact  that  the  pressure  at  the  suction  intake  decreases  as  the  flow 
increases,  we  see  that  the  following  state  of  affairs  might  exist. 
As  vapor  is  liberated  and  fills  part  of  the  space,  the  rate  of  dis- 
charge decreases.  This  causes  the  pressure  to  rise,  the  vapor 
again  becomes  liquid,  the  pipe  is  filled  with  water  and  the  dis- 
charge increases.  But  as  it  does  so  the  pressure  drops  again  and 
thus  a  pulsation  of  flow  is  set  up.  If  there  is 
just  about  a  balance  this  pulsation  will  be  per- 
ceptible to  the  ear  only.  If  the  pressure  is 
further  decreased  the  pulsation  is  sufficient  to 
cause  the  suction  line  and  pump  to  vibrate. 
If  the  pressure  is  made  still  lower,  the  flow 
will  finally  cease. 

About  90  per  cent,  of  centrifugal  pump 
trouble  will  be  found  on  the  suction  side  of  the 
pump.  The  rest  of  the  trouble  is  largely  due 
to  the  end  thrust. 

17.  Piping  Connections. — In  order  to  mini- 
mize._th_e  suction-pipe  lossesTTTmay  be  desir- 
able to  have  it  larger  than  that  of  the  suction- 
pipe  connection.  Also  it  may  be  desirable 
to  have  the  discharge  pipe  much  larger  than 
that  of  the  discharge  connection  in  order  to 
reduce  the  friction  head  against  which  the 
pump  has  to  work.  For  making  these  con- 
nections so  as  to  prevent  losses  due  to  abrupt  change  of  cross  sec- 
tion, the  taper  connections  A  and  B  in  Fig.  44  are  very  desirable. 
Not  only  do  the  larger  suction  and  discharge  pipes  reduce  the 
friction  head  and  thus  improve  the  overall  pumping  efficiency 
but,  as  will  be  seen  later,  the  lower  head  that  the  pump  will  have 
to  develop  will  enable  its  efficiency  alone  to  be  somewhat  higher. 
18.  Pumps  in  Series  and  in  Parallel. — Two  or  more  pumps 
may  sometimes  be  operated  in  series  or  in  parallel,  resulting  in 
great  flexibility  of  service.  If  two  pumps,  for  instance,  with 
identical  characteristics  are  operated  in  series  the  discharge  will 
be  the  same  and  the  head  developed  twice  as  much  as  with  either 
one  of  them  alone.  If  they  are  operated  in  parallel  the  head  will 


FIG.    44.— Taper 
pipe  connections. 


INSTALLATION  AND  OPERATION  43 

be  the  same  and  the  discharge  twice  as  much  with  either  one 
alone. 

It  would  seem  as  if  the  efficiency  should  be  the  same  for  the 
pumps  combined  as  that  of  one  of  them  alone.  But  for  two  or 
more  pumps  in  parallel  the  efficiency  appears  to  be  a  few  per  cent, 
less  than  that  of  the  individual  pumps.1  This  is  undoubtedly 
due  to  the  fact  that  no  two  pumps  have  precisely  the  same 
characteristics,  due  to  necessary  variations  in  workmanship, 
and  thus  the  water  is  not  equally  divided  between  them.  Prob- 
ably each  one  is  working  with  a  discharge  which  is  not  the  one 
for  which  its  efficiency  is  the  highest. 

19.  Operating  a  Centrifugal  Pump. — In  starting  up  a  cen- 
trifugal pump  the  first  thing  to  do  is  to  see  that  the  discharge 
valve  is  closed.  This  is  not  only  necessary  in  some  cases  in  order 
to  prime  the  pump  but  it  prevents  overloading  the  motor,  since 
the  power  at  shut-off  is  less  than  for  normal  delivery.  After 
the  pump  is  primed  and  all  the  air  expelled,  the  pump  may  be 
started  and  brought  up  to  speed.  Then  the  discharge  valve 
may  be  slowly  opened,  so  as  not  to  throw  a  sudden  load  on  the 
motor,  until  it  is  wide  open  or  at  least  until  the  desired  discharge 
is  obtained.  These  precautions  in  starting  are  not  neces 
with  all  types  of  motors.  After  the  pump  is  running  it  is  only 
necessary  to  see  that  the  bearings  are  supplied 'with  oil,  that  the 
packing  glands  are  properly  adjusted  so  as  to  neither  leak  too 
much  nor  on  the  other  hand  to  run  hot,  that  the  suction  gland  is 
supplied  with  water  for  the  water  seal,  and  that  sufficient  water 
is  circulated  through  the  thrust  bearing,  if  there  is  one,  to  keep 
it  cool. 

When  it  is  desired  to  shut  down  the  pump,  it  is  best  to  first  close 
the  discharge  valve,  then  to  throw  off  the  power.  This  reduces 
the  amount  of  power  that  will  be  abruptly  dropped  from  the  line 
and  also  prevents  the  flow  in  the  discharge  pipe  from  being  sud- 
denly stopped.  If  the  pipe  line  is  long  this  might  otherwise 
create  a  pressure  surge.  It  is  often  advisable,  in  the  case  of  a 
long  pipe  line,  to  protect  the  pump  by  means  of  a  check  valve  on 
the  discharge  side. 

1  R.  C.  Carpenter,  "The  High-pressure  Fire  Service  Pumps  of  Manhattan 
Borough,  City  of  New  York,"  Trans.  A.S.M.E.,  Vol.  31,  page  437  (1909). 


CHAPTER  IV 
GENERAL  THEORY 

20.  Notation. — The  following  notation  will  be  employed: 
V    =  absolute  velocity  of  water  (or  relative  to  earth)  (ft.  per  sec.) 
v     =  velocity  of  water  relative  to  impeller  (ft.  per  sec.) 
u     =  linear  velocity  of  a  point  of  the  impeller  (ft.  per  sec.) 
r     =  radius  to  any  point  from  the  axis  of  rotation  (ft.) 
z     =  elevation  above  any  arbitrary  datum  plane  (ft.) 
A    =  angle  between  V  and  u  (Fig.  45) 
a     =  angle  between  v  and  —  u  (Fig.  45) 
s     =  tangential  component  of  V,  =  V  cos  A 
F    =  area  of  streams   normal   to  the  direction  of  flow  in  the 

stationary  passages  (sq.  ft.) 

/     =  area  of  streams  normal  to  the  direction  of  flow  in  the  rotat- 
ing passages  (sq.  ft.)  (Fig.  46) 
D    =  outer  diameter  of  impeller  in  inches 
B    =  width  of  impeller  at  periphery  in  inches 
q     —  rate  of  discharge  in  cu.  ft.  per  sec. 
w    =  weight  of  a  cu.  ft.  of  water  (taken  as  62.4  Ib.) 
W  =  pounds  of  water  per  sec.  =  wq 
p     =  intensity  of  pressure  in  feet  of  water 
H    =  total  head  =  z  +  p  +  V2/2g 
h     =  head  developed  by  pump 
In!    =  head  lost  within  the  pump 
H'  =  any  other  loss  of  head 

h"  =  head  imparted  to  the  water  by  the  impeller  =  h  -f-  h' 
<f>    =  ratio  of  peripheral  speed  to  \/2gh  —  u2/\/2gh 
N    =  revolutions  per  minute 

co     =  angular  velocity  =  2irN/6Q  =  u/r  (radians  per  sec.) 
e     =  efficiency  (Art.  29) 
g     =  acceleration  of  gravity  =  32.2  ft.  per  sec.  per  sec. 

Values  of  quantities  at  specific  points  will  be  indicated  by  sub- 
scripts. (See  Fig.  1.)  The  subscript  (s)  will  refer  to  the  stream  in 
the  suction  pipe  close  to  the  pump,  the  subscript  (i)  will  refer  to 
values  at  entrance  to  the  impeller,  subscript  (2)  at  exit  from  the 
impeller,  subscript  (3)  in  the  case,  and  (d)  in  the  discharge  pipe. 

44 


GENERAL  THEORY 


45 


The  notation  as  given  in  regard  to  velocities  and  angles  refers 
to  values  as  determined  by  the  vector  diagrams.  Whenever 
the  conditions  are  such  that  a  velocity  or  direction  must  be  differ- 
ent from  that  given  by  the  vector  diagram,  the  resulting  values 
will  be  signified  by  the  use  of  a  prime  (').  (See  Fig.  57.) 

21.  Relation  between  Absolute  and  Relative  Velocities. — The 
absolute  velocity  of  a  body  is  its  velocity  relative  to  the  earth. 
The  relative  velocity  of  a  body  is  its  velocity  relative  to  some 
other  body  which  may  itself  be  in  motion  relative  to  the  earth. 
The  absolute  velocity  of  the  first  body  is  the  vector  sum  of  its 
velocity  relative  to  the  second  body  and  the  absolute  velocity  of 


FIG.  45. — Relation  between  absolute  and  relative  velocities. 

the  second  body.     The  relation  between  the  three  is  shown  in 
Fig.    45. 1)2  . 

1  The  angle  between  two  vectors  is  properly  the  angle  between  their 
positive  directions.     In  the  author's  "Hydraulic  Turbines"  this  convention 
is  adhered  to  so  that  a  is  used  to  designate  the  angle  between  u  and  v.     In 
such  work  this  angle  may  be  either  acute  or  obtuse,  but  with  centrifugal 
pumps  this  angle  is  almost  always  greater  than  90°.     For  this  reason  it 
has  been  thought  more  convenient  in  this  book  to  use  the  angle  between 
v  and  —  u.     Evidently  in  the  left-hand  diagram  of  Fig.  45,  cos  a  will  be 
negative,  while  it  will  be  positive  in  the  other  two. 

2  A  clearer  conception  of  absolute  and  relative  motion  may  be  had  by 
considering  paths  traversed.     Suppose  that  a  rectangular  raft  is  moving 
down  a  stream  with  a  uniform  velocity  u.     After  an  interval  of  time   A  t 
the  raft  may  be  represented  in  a  second  position.     Each  point  on  the  raft 
will  have  traveled  a  distance  u  A  L     Supposed  that  a  man  on  the  raft  has 
moved  during  this  interval  of  time  from  one  corner  of  the  raft  to  a  diagonally 
opposite  corner.     Relative  to  the  raft  his  path  is  a  straight  line  which  is  a 
diagonal  of  the  raft.     But  relative  to  the  earth  his  path  will  be  a  different 
line  inasmuch  as  the  corner  where  he  stops  is  not  in  the  same  place  that  it 
was  when  he  started.     If  he  moves  across  the  raft  with  a  uniform  velocity 
v  relative  to  it  the  length  of  his  relative  path  will  be  v  A  t.     Since  u  and  v  are 
uniform  during  this  time  interval,  his  absolute  velocity  T  is  also  uniform 
and  his  absolute  path  is  a  straight  line  of  length  FAf.     Since  the  velocities 
are  uniform,  by  dividing  by   AZ,  the  lengths  of  the  paths  may  represent 
velocities  at  any  instant. 


46  CENTRIFUGAL  PUMPS 

The  radial  component  of  the  velocity  is  seen  to  be 

Vr  =  V  sin  A  =  v  sin  a  (1) 

The  tangential  component  of  V  is 

s  =  V  cos  A  =  u  —  v  cos  a  (2) 

22.  Equation  of  Continuity  .—By  F  or  /  is  meant  the  total  area 
of  all  the  streams  into  which  the  entire  flow  may  be  divided. 
Thus  /2,  for  example,  will  equal  the  total  area  of  all  the  streams 
leaving  the  impeller  measured  normal  to  v2,  while  F\  will  denote 
the  total  area  of  all  the  streams  in  the  diffusion  vane  channels 
measured  normal  to  V2. 


FIG.  46. — Velocity  diagrams. 

In  Fig.  46,  if  n  denote  the  number  of  impeller  vanes,  the  area  /2 
for  example,  could  be  computed  as  follows: 

/2  =  n  X  AC  XB/144  (3) 

where  AC  =  the  normal  distance  across  the  impeller  passage 
in  inches  and  B  =  impeller  width  in  inches  (Fig.  17).  Or  if 
the  thickness  of  the  vanes  in  inches  be  denoted  by  t,  the  area 
could  be  computed  as 

/2  =  (irD  sin  a2  -  n£)£/144  (4) 

The  latter  method  may  be  slightly  more  logical  but  the  former 
is  more  generally  used.  In  the  usual  case  the  two  methods  give 
results  which  differ  but  little  from  each  other. 


GENERAL  THEORY  47 

If  the  vane  curves  are  involutes  the  two  methods  above  will 
give  identical  results.  This  is  because  the  distance  between  two 
adjacent  vanes  remains  constant  as  may  be  seen  in  Fig.  108(6), 
page  172,  where  A  and  A'  trace  involutes  as  the  cord  CAA'  may 
be  conceived  to  be  wound  around  the  base  circle  of  radius  OC. 
In  such  event  we  have  in  Fig.  46  that 

AC  +  t  =  arc  AB  sin  a2  =  (irD/ri)  sin  a2 
Therefore,  n  X  A  C  =  TrD  sin  a2  —  nt 

If  the  flow  is  steady  and  the  rate  of  rotation  uniform,  the  equa- 
tion of  continuity  may  be  applied.  This  states  that  the  rate  of 
flow  past  all  sections  is  constant  or  that  q  =  FV  =  fv  =  constant 
and  in  particular 

q  =  fivi  =  M  =  F,V2  =  F'2V'Z  (5) 

23.  General  Equation  of  Energy. — Energy  may  be  transmitted 
across  a  section  of  a  flowing  stream  in  any  or  all  of  the  three  forms 
known  as  potential  energy,  pressure  energy,  .or  kinetic  energy. 
Head  may  be  defined  as  the  amount  of  energy  per  unit  weight 
of  water.  The  total  head  at  any  section  will  be  given  by 

H  =  z  +  p  +  V*/2g  (6) 

There  can  be  no  flow  without  some  loss  of  energy  by  friction  so 
that  the  total  head  must  decrease  in  the  direction  of  flow  by  the 
amount  of  head  lost  or 

H,  -  H2  =  H'  (7) 

Subscripts  d)  and  (2)  are  here  used  to  designate  any  two  points 
whatsoever. 

In  flowing  through  the  impeller  of  a  centrifugal  pump,  the 
water  loses  energy  due  to  various  friction  losses.  The  energy 
lost  is  dissipated  in  the  form  of  heat.  But  the  water  must  receive 
from  the  impeller  vanes  a  greater  quantity  of  energy  than  that 
which  is  lost.  We  denote  by  h"  the  head  imparted  to  the  water 
by  the  vanes.  Thus  the  preceding  equation  may  be  written 
(since  h"  is  a  negative  loss), 

Hi  -  H2  =  h'  -  h"  (8) 

Again  the  subscripts  may  denote  any  two  points  whatsoever  as 
long  as  h'  is  understood  to  mean  the  total  loss  of  head  between  the 
two  points.  In  (7)  HI  must  be  greater  than  H2  unless  there  is 


48 


CENTRIFUGAL  PUMPS 


a  pump  between  the  two  points.  If  there  is  a  pump  between  the 
two  points,  then  in  general  Hz  will  be  the  larger.  In  our  notation 
we  always  presume  that  water  flows  from  (1)  to  (2). 

24.  Losses  of  Head  in  Pipes. — The  most  important  loss  in  a 
pipe  line  of  any  length  is  that  due  to  friction  along  the  walls  of 
the  pipe  and  to  internal  friction  of  the  particles  of  water  against 
each  other.1  This  loss  may  be  given  by  the  formula 

Hf  =  m(l/d)V*/2g  (9) 

where  m  is  a  friction  factor,  and  (l/d)  is  the  ratio  of  the  length  of 
the  pipe  to  its  diameter.  Since  this  ratio  is  an  abstract  number, 
it  follows  that  both  I  and  d  must  be  in  the  same  units. 


= 


FIG.  47. — Entrance  and  discharge  losses. 

The  factor  m  for  new  clean  cast-iron  pipe  may  be  determined  by 
m  =  0.02  +  0.02/d  (10) 

but  in  the  latter  formula  d  must  be  in  inches,  otherwise  we  should 
have  to  change  the  numerator.  For  old  pipe  these  values  need 
to  be  increased  and  may  even  be  twice  the  value  given  by  the 
formula.  The  factor  m  would  also  be  larger  with  riveted  steel 
pipe  and  less  with  wood-stave  pipe  than  would  be  the  case  with 
cast-iron  pipe.  In  any  event  the  choice  of  a  value  of  m  is  largely 
a  matter  of  judgment. 

At  entrance  to  a  pipe  as  shown  in  Fig.  47 (a),  there  is  a  loss  of 
head  of  approximately  1.0V2/2g.  A  foot  valve  or  other  device 
on  the  end  of  the  pipe  might  increase  this  value.  If  the  end  of 
the  pipe  is  flush  with  the  side  as  shown  in  (6),  the  loss  is  approxi- 
mately 0.5F2/2#.  By  rounding  the  mouth  of  the  pipe  and  giv- 
ing it  a  taper  for  a  few  feet  so  that  there  is  no  abrupt  change  of 
velocity  at  entrance  this  loss  may  be  reduced  practically  to  zero. 

1  For  more  complete  information  on  this  subject  consult  Hughes  and 
Safford,  " Hydraulics,"  Chap.  XV;  Russell,  " Hydraulics,"  Chap.  VIII; 
Hoskins,  "Hydraulics,"  Chap.  IX  and  other  standard  works. 


GENERAL  THEORY 


49 


At  discharge  there  is  a  loss  of  head  of  l.QV2/2g.  This  is  true 
whether  the  pipe  projects  as  shown  in  Fig.  47  (c)  or  whether  it 
does  not.  That  this  is  the  loss  may  readily  be  seen  by  noting 
that  Hi  =  0  +  a  +  V*/2g  and  H2  =  0  +  a  +  0,  where  a 
denotes  the  pressure  at  (1)  and  (2).  The  body  of  water  is  sup- 
posed to  be  so  large  that  the 
velocity  at  (2)  is  negligible. 
From  (7)  H'  =  #1  -  #2  = 


Where  there  is  a  sudden  FIG.  48.  —  Abrupt  changes  in  velocity. 
contraction  of  the  stream  as 

in  Fig.  48  (a),  there  is  a  loss  of  head  of  Hf  =  kV^/Zg,  where  k 
is  an  experimental  factor,  which  increases  as  the  ratio  of  the 
two  areas  departs  from  unity.  The  value  of  k  is  usually  less 
than  unity. 

Where  there  is  an  abrupt  enlargement  of  the  stream  as  in 
Fig.  48(6),  theory  and  experiment  indicate  that  the  loss  may  be 
approximately  represented  by 

H'  =  (V,  -  V,Y/2g 


FIG.  49. — Head  against  which  a  pump  works. 

25.  Head  Developed  by  Pump. — The  head  developed  by  a 
pump  is  equal  to  the  actual  vertical  lift  plus  all  losses  in  the 
piping  (but  not  within  the  pump  itself).  Thus  for  Fig.  49 

/h  =  z  +  H'  (H) 

If  the  pipe  discharges  into  the  air  at  a  height^  above  the  suc- 
tion level,  the  value  of  the  head  is  the  same  as  for  the  case 
shown  in  the  figure.  In  either  event  the  velocity  head  at  the 
mouth  of  the  pipe  should  be  included  in  H'  as  a  discharge  loss. 

4 


50  CENTRIFUGAL  PUMPS 

Even  in  case  this  velocity  head  should  be  useful  it  is  necessary 
to  include  it  in  computing  the  head,  since  it  represents  an  ex- 
penditure of  energy  by  the  pump.  But  in  the  latter  event  the 
useful  work  done  is  proportional  to  z  +  V2/2g  rather  than  z  alone. 

The  vertical  lift  z  is  sometimes  called  static  head  while  the 
total  head  against  which  the  pump  works,  z  -\-  H',  is  called  dy- 
namic head. 

Evidently  the  head  actually  delivered  by  the  pump  is  equal  to 
the  difference  between  the  head  with  which  the  water  enters 
and  that  with  which  it  leaves.  Thus 

h  =  zd  -  zs  +  Pd  -  ps  +  (V/  -  Vs*)/2g  (12) 

In  general  the  water  enters  the  pump  under  a  pressure  which 
is  less  than  that  of  the  atmosphere,  in  which  case  ps  will  be  nega- 
tive in  value.  Frequently  the  suction  pipe  is  a  size  larger  than 
the  discharge  pipe,  but  if  they  are  of  the  same  size  the  velocity 
head  correction  drops  out  of  equation  (12).  In  such  an  event 
the  total  value  of  h  may  be  shown  graphically  as  in  Fig.  49,  for 
it  is  the  vertical  distance  between  the  summits  of  the  two  water 
columns  there  represented.1 

26.  Centrifugal  Action  or  Forced  Vortex. — If  a  vessel  con- 
taining a  liquid  is  rotated  about  its  axis,  the  liquid  will  tend  to 
rotate  at  the  same  speed.  If  we  take  an  elementary  volume 
whose  length  along  the  radius  is  dr  and  whose  area  normal  to  the 
radius  is  dF,  we  have  an  elementary  mass  wdFdr/g  moving  in  a 
circular  path.  This  mass  has  an  acceleration  directed  toward 
the  axis  of  rotation  whose  value  is  uz/r  or  coV.  Consequently 
the  value  of  the  accelerating  force  is  (wdFdr/g)u?r.  The 
intensity  of  pressure  on  the  two  faces  of  the  elementary  volume 
differs  by  wdpr  (Ib.  per  sq.  ft.).  The  value  of  the  resultant  force 
is  therefore  wdprdF.  Consequently 

wdprdF  =  (w  dFdr/g)  coV 

dpr  =  (u^/g}rdr 

1  The  question  is  often  raised  as  to  why  Vs2/2g  should  be  deducted  in 
(12),  since  the  energy  represented  by  it  has  really  been  imparted  by  the 
pump.  Of  course  (12)  is  a  direct  application  of  (8),  but  aside  from  that  it 
may  be  said  that  the  velocity  head  affects  the  value  of  p6.  Applying  (7) 
between  suction  level  and  (s)  and  with  the  surface  of  the  suction  level  as 
datum, 

—  ps  —  Vs~/2g  =  zs  +  suction  pipe  losses. 

Combining  this  with  (12),  h  =  Zd  +  Pd  +  Vd2/2g  +  suction  pipe  losses. 
It  would  be  as  unreasonable  to  omit  Vsz/2g  in  (12)  as  to  omit  ps. 


GENERAL  THEORY 


51 


But  this  expression  shows  only  the  difference  of  pressure  along 
the  radius  and  in  the  same  horizontal  plane.  If  we  move  along 
a  path  parallel  to  the  vertical  axis  of 
rotation  so  that  the  radius  is  constant, 
the  pressure  decreases  directly  as  the 
elevation  increases.  Thus 

dpz  =  —  dz 

The  variation  of  the  intensity  of  pres- 
sure in  any  direction  whatsoever  may 
be  found  by  combining  the  two  pre- 
ceding equations.  Thus,  in  general, 


dp  =  —  dz+  (u2/g)rd 

i 

i'cfc 


(13) 


dp)dE 


FIG.  50. — Forced  vortex. 


FIG.  51. — Crude  centrifugal  pump. 

To  find  the  equation  of  the  free  surface  or  any  surface  of  equal 
pressure  we  need  only  place  dp  equal  to  zero.     We  then  have 


52  CENTRIFUGAL  PUMPS 

fdz  =  (a*/g)frdr 

z  =  r2co2/2gr  +  constant 

To  determine  the  constant  we  may  assume  that  z  =  0  where 
r  =  0.     Thus  the  constant  =  0.     Therefore 

z  =  r2a>2/2g  =  u2/2g  (14) 

This  shows  that  the  free  surface  or  any  surface  of  equal  pressure 
is  a  paraboloid,  since  the  above  is  the  equation  of  a  parabola. 

To  find  the  variation  of  the  pressure  between  two  points  at 
the  same  elevation  take  dz  —  0.     Thus  as  above  we  get 

p  =  r2o>2/20  =  u2/2g  '~r.  /? 

*• 
or  integrating  between  specified  limits 

2  -  Pi  =  (r22  -  rtfa>*/2g  =  (u<?  -  utf/2g  (15) 


p2  -  Pi  =    r2    -  ra>g  =    u<    -  ug 

For  the  difference  in  pressure  between  any  two  points  we 
must  integrate  (13)  from  which  we  get 

P2  -  Pi  =  zi  -  22  +  u22/2g  -  Ul*/2g  (16) 

If  water  in  a  closed  chamber  is  set  in  motion  by  a  paddle  wheel 
as  in  Fig.  51,  there  will  be  an  increase  in  the  pressure  from  the 
center  to  the  circumference.  By  (16)  this  pressure  difference 
may  be  seen  to  be  u22/2g,  where  u2  is  the  velocity  of  the  tips  of 
the  paddle  or  the  velocity  of  the  water  at  the  outer  radius.  If  the 
water  from  this  chamber  is  allowed  to  enter  a  vertical  pipe  such 
as  the  right-hand  piezometer  tube  in  Fig.  51,  water  will  rise  in 
it  to  such  a  height  that 

h  =  u2*/2g  (17) 

If  the  height  of  the  tubes  were  less  than  this,  water  would  flow  out 
and  we  should  have  a  crude  centifugal  pump. 

The  above  value  of  h  is  commonly  said  to  be  the  height  of  a 
column  of  water  sustained  by  "  centrifugal  force."  It  is  more 
properly  the  height  required  to  produce  the  pressure  necessary 
to  give  the  water  its  centripetal  acceleration. 

27.  Free  Vortex.  —  Where  energy  is  imparted  to  the  water  as  in 
the  preceding  case,  we  have  a  forced  vortex.  Where  no  energy 
is  imparted,  we  have  a  free  vortex.  We  shall  first  consider  a  pure 
radial  flow  between  two  parallel  plates.  In  such  a  case  Vr  and 
V  are  identical.  If  6  =  the  distance  between  the  plates,  by  the 
equation  of  continuity  we  have 

q  =  2*Ti&  X  Vi  =  2-jrr2b  X  Vz 


GENERAL  THEORY 
From  this  it  is  seen  that  V  (or  Vr)  varies  as  1/r,  or 


53 


Neglecting  losses  of  energy,  #  =  z  +  p  +  F2/2<7  =  constant  or 

H  =  p,  +  7!V2flr  =  p2  +  F22/2</ 
P2  =  H  -  (r,/rzyVS/2g 

The  variation  of  pressure  and  velocity  head  with  r  is  shown  in 
Fig.  52. 

A  free  circular  vortex  consists  of  a  body  of  water  in  rotation 
without  any  appreciable  flow.  Thus  the  stream  lines  are  concen- 
tric circles  and  s  and  V  are  identical.  In  Art.  35  it  is  shown 
that  torque  equals  the  time  rate  of  change  of  angular  momentum. 
Since,  neglecting  frictional  resistance,  no  torque  is  exerted,  it 
follows  that  the  angular  mo- 
mentum must  be  constant. 
But  angular  momentum  is 
the  product  of  the  mass  times 
s  times  r.  Therefore  s  or  V 
varies  as  1/r.  Since  no  energy 
is  imparted,  neglecting  fric- 
tional resistance,  we  have 
throughout  the  mass  H  —  z 
+  P  +  V2/2g  =  constant.  It 

is  thus  seen  that  our  equations  are  exactly  the  same  as  for  a  pure 
radial  flow.  The  only  difference  between  the  two  is  that  in  the 
one  case  V  =  Vr,  in  the  other  case,  V  =  s. 

A  free  spiral  vortex  is  a  combination  of  the  two  previous  cases. 
Since  V2  =  Vr2  +  s2,  it  follows  that  in  the  case  of  flow  along  a 
spiral  path  V  varies  as  1/r.  Also  since  V,  Vr,  and  s  all  vary  as 
1/r,  it  may  be  seen  that  the  angle  A  is  constant  for  all  values  of  r. 
Thus  the  stream  line  must  be  a  logarithmic  spiral,  the  equation  of 
which  is  r  =  eke,  where  e  =  2.7183,  k  =  constant,  and  0  =  angle 
of  the  radius  vector  with  an  initial  position. 

For  a  free  spiral  vortex  the  equations  are  the  same  as  those  for 
pure  radial  flow,  except  that  the  actual  velocity  is  riot  radial. 
Thus 

p2  =  H  -  (ri/rt)2Vi2/2g 

=  Pi  +  [1  -  (ri/r2)WA7  (18) 

The  last  expression  in  the  above  equation  is  the  maximum  possible 
gain  of  pressure  due  to  a  vortex  chamber.  Actually,  owing  to 


FIG.  52. — Free  vortex. 


54  CENTRIFUGAL  PUMPS 

frictional  losses  and  instability  of  flow  resulting  in  a  departure 
from  the  stream  lines  assumed,  the  pressure  increase  will  be  much 


28.  Illustration  of  Centrifugal  Pump  Losses. — In  order  to  make 
clear  the  exact  meaning  of  certain  terms  used,  a  numerical  illus- 
tration will  now  be  given.     Suppose  that  it  takes  80.0  h.p.  to  run 
a  certain  centrifugal  pump.     This  power  is  commonly  called 
brake  horse-power,  the  reason  for  this  usage  being  that  it  is  the 
brake  horse-power  or  developed  horse-power  of  the  engine,  turbine, 
or  motor  that  drives  the  pump.     Assume  that  the  friction  of  the 
bearings  arid  the  drag  of  the  impeller  through  the  water  surround- 
ing it  is  5.0  h.p.     This  leaves  75.0  h.p.  to  be  delivered  to  the  water 
by  the  impeller.     We  shall  suppose  that  11.0  cu.  ft.  of  water 
per  sec.  is  circulated  through  the  impeller  but  that  the  pump 
actually  delivers  only  10.0  cu.  ft.  per  sec.,  the  other  1.0  cu.  ft.  be- 
ing "  short  circuited,"  that  is  leaking  back  past  the  clearance 
rings,  etc.     The  75.0  h.p.  will  then  be  divided  up  into  6.8  h.p.  for 
this  leakage  and  68.2  h.p.  for  the  10  cu.  ft.  per  sec.  actually  de- 
livered.    But  the  water  actually  delivered  suffers  certain  hydrau- 
lic friction  losses  within  the  impeller  and  also  after  leaving  the 
impeller,  which  we  shall  take  as  being  11.4  h.p.     This  leaves 
68.2  —  11.4  =  56.8  h.p.  as  the  actual  useful  output  of  the  pump. 
The   latter   quantity   is   commonly   called   water   horse-power. 

Since  power  is  a  function  of  rate  of  flow  and  of  head,  it  follows 
that  definite  values  of  head  must  be  associated  with  some  of  the 
values  of  horse-power  in  the  preceding  paragraph.  Thus  to  de- 
liver 75.0  h.p.  to  11.0  cu.  ft.  of  water  per  sec.  means  that  the 
impeller  must  impart  to  the  water  a  head  of  60.0  ft.  And  if  10.0 
cu.  ft.  of  water  per  sec.  suffers  a  loss  of  11.4  h.p.  it  can  only  mean 
that  there  is  a  loss  of  head  of  10.0  ft.  Thus  the  actual  head  de- 
veloped by  the  pump  is  60.0  —  10.0  =  50.0  ft.  This  last  expres- 
sion in  general  terms  is  h"  —  h'  =  h. 

29.  Definitions  of  Efficiencies. — The  word  " efficiency"  with- 
out any  qualification  will  always  be  understood  to  mean  gross  or 
total  efficiency.     It  is  the  ratio  of  the  water  horse-power  to  the 
brake    horse-power.     That   is 

e  =  W.h.p./B.h.p.  (19) 

Mechanical  efficiency  is  the  ratio  between  the  power  actually 
delivered  to  (not  by)  the  water  and  the  power  supplied  to  the 


GENERAL  THEORY  55 

pump.     If  q  =  actual  rate  of  pump  discharge  and  qf  =  the  rate 
of  leakage, 


m          ~500  ---  /?•*•£• 

Hydraulic  efficiency  is  the  ratio  of  the  power  actually  delivered 
by  the  water  to  the  power  imparted  by  the  impeller  to  the  water 
actually  discharged  by  the  pump.  That  is 


eh  =  W.K.p./          =  h/h"  (21) 


Volumetric  efficiency  is  the  ratio  of  the  water  actually  delivered 
by  the  pump  to  that  discharged  by  the  impeller.  It  is  analogous 
to  the  "1.00-slip"  used  in  reciprocating  pump  work. 

e*  =  Q/(q  +  ?')  (22) 

Naturally  it  follows  that  the  total  efficiency  is  the  product  of 
these  three  separate  factors.  That  is 

e  =  em  X  ch  X  e,  (23) 

In  the  numerical  case  given  in  the  preceding  article,  these 
various  efficiencies  are:  em  =  75.0/80.0  =  0.938,  eh  =  56.8/68.2 
=  50/60  =  0.833,  ev  =  68.2/75.0  =  10/11  =  0.910,  e  = 
56.8/80.0  =  0.938  X  0.833  X  0.910  =  0.710. 

30.  Duty.  —  The  term  "duty"  is  an  expression  that  has  long 
been  used  for  pumping  engines  and  has  been  variously  defined. 
First  it  was  the  number  of  foot  pounds  of  work  done  per  bushel 
of  coal  burned,  then  per  100  Ib.  of  coal,  then  per  1,000  Ib.  of 
steam  supplied  by  the  boiler,  and  last  per  1,000,000  British 
thermal  units  supplied  by  the  boiler.  It  will  be  seen  that  all  of 
these  quantities  are  approximately  equivalent  to  each  other. 
The  last  term  is  the  most  exact  but  that  is  even  open  to  the  objec- 
tion that  the  steam  pressure  or  the  quality  of  the  steam  must 
make  a  difference  in  operation,  even  when  the  total  number  of 
heat  units  is  the  same. 

The  term  "  duty  "  is  sometimes  applied  to  a  motor-driven  pump, 
but  in  such  a  case  it  must  be  noted  that  there  is  no  fair  comparison 
between  it  and  a  steam-driven  pump  in  terms  of  duty  without 
suitable  qualification.  For  the  motor-driven  pump  we  must 
take  the  duty  as  the  foot  pounds  of  work  done  per  million  B.t.u. 
supplied  to  the  motor.  Thus  our  base  is  entirely  different  from 
that  of  the  former  case. 


56  CENTRIFUGAL  PUMPS 

Since  1,000,000  B.t.u.  =  778,000,000  ft.  lb.,  we 'may  write 
Duty  =  778,000,000  X  Pump  Eff.  X  Engine  Thermal  Eff.  (24) 
The  thermal  efficiencies  of  the  most  economical  steam  engines 
or  turbines  usually  range  from  10  to  20  per  cent.  For  the  motor- 
driven  pump  we  should  have  to  substitute  the  motor  efficiency 
in  place  of  the  thermal  efficiency  in  the  above  formula.  The 
motor  efficiency  is  usually  from  80  to  90  per  cent. 

Since  pump  efficiency  =  W.h.p./B.h.p.,  and  the  engine  thermal 
efficiency  =  (B.h.p.  X  2,545)/lb.  steam  per  hr.  X  B.t.u.  per  lb., 
we  have  per  1,000,000  B.t.u. 

W.h.p.  X  1,980,000,000,000 
Lb.  steam  per  hr.  X  B.t.u.  per  lb. 

Dut     =        Pump  Efficiency  X  1,980,000,000,000 

Lb.  steam  per  b.h. p.  per  hr.  X  B.t.u.  per  lb. 

To  obtain  duty  per  1,000  lb.  of  steam  omit  the  B.t.u.  per  lb. 
in  (22)  or  (23)  and  divide  the  numerator  by  1,000. 

The  highest  duties  attained  by  centrifugal  steam-driven  pump- 
ing units  are  slightly  above  100,000,000  ft.  lb. 

31.  Abbreviations. — The    following    abbreviations    are    com- 
monly employed : 

G.P.M.  =  gallons  per  min.1 
R.p.m.    =  revolutions  per  min. 
B.h.p.     =  brake  horse-power. 
W.h.p.    =  water  horse-power. 
K.w.       =  kilowatts. 

32.  Conversion  Factors. 

1  U.S.  gallon  =  0.134  cu.  ft.  =  8.33  lb.  of  water. 
1  Imperial  gallon  =  1.2  U.S.  gallons  =  10  lb.  of  water. 
1  cu.  ft.  =  7.48  U.S.  gallons.  =  62.4  lb.  of  water. 
1  cu.  ft.  per  sec.  =  448  G.P.M. 

=  647,000  gal.  per  24  hr. 
1,000,000  gal.  per  24  hr.  =  1.545  cu.  ft.  per  sec. 

=  695  G.P.M. 

1,000  lb.  of  water  per  hr.  =  2  G.P.M. 
1  lb.  per  sq.  in.  =  2.308  ft.  of  water. 
1  in.  of  mercury  =  1.132  ft.  of  water. 
1  h.p.  =  550  ft.  lb.  per  sec.  =  0.746  k.w. 

1  Throughout  this  work  the  U.S.  gallon  is  used.  The  U.S.  gallon  = 
231  cu.  in.  =  0.134  cu.  ft.  =  8.33  lb.  of  water. 


GENERAL  THEORY  57 

33.  Useful  Formulas. 


8.33  X  G.P.M.  X  h        G.P.M.  X  h 
33,000  3,960 

If  the  velocity  of  flow  in  a  pipe  be  V  in  ft.  per  sec.  and  the  diame- 
ter of  the  pipe  in  inches  be  d, 

Vd2 

*¥m$ 

G.P.M.  =  2.443  Vd2  (30) 

h        V2        -_<z2        (G.P.M.) 
hv=2g   '-"   523^    :     ^85^~ 

V  =  8.025\//^  (32) 

34.  PROBLEMS 

1.  The  peripheral  velocity  of  a  point  on  an  impeller  is  100  ft.  per  sec. 
The  relative  velocity  of  the  water  at  that  point  is  20  ft.  per  sec.  and  the 
angle  a  =  30°.     What  is  the  magnitude  and  direction  of  the   absolute 
velocity? 

Ans.  V  =  83.3  ft.  per  sec.,  A  =  6°  55'. 

2.  What  is  the  radial  component  of  the  velocity  in  (1)?     What  is  the 
tangential  component? 

.Ans.  Vr  =  vr  =  10  ft.  per  sec.,  s  =  82.68  ft.  per  sec. 

3.  If  the  relative  velocity  v2  =  20  ft.  per  sec.  and  the  area  /2  =  0.400  sq. 
ft.,  what  must  be  the  value  of  F2  if  Vz  =  83.3  ft.  per  sec.? 

Ans.  0.096  sq.  ft. 

4.  In  Fig.  49  suppose  the  diameter  of  the  pipe  is  10  in.,  the  length  of  the 
suction  pipe  is  10  ft.,  the  length  of  the.  discharge  pipe  is  800  ft.,  andz  =  66.0 
ft.     Suppose  that  Zd  =  8  ft.  and  zs  =  6  ft.     If  the  pump  delivers  6.0  cu.  ft. 
of  water  per  sec.,  find  the  total  head  pumped  against,  pressure  head  at  s 
and  d,  and  the  water  horse-power.     (Assume  new  clean  cast-iron  pipe.) 

Ans.  h  =  110ft.,  p,  =  -  10.28ft.,  pd  =  97.72ft.,  75.0  h.p. 

5.  The  diameter  of  the  discharge  pipe  of  a  centrifugal  pump  =6  in., 
that  of  the  suction  pipe  =  8  in.     Pressure  gage  at  d  reads  30  Ib.  per  sq.  in.? 
vacuum  gage  at  s  reads  10  in.  of  mercury.     The  pressure  gage  is  3  ft.  above 
the  vacuum  gage.     If  q  =  3.0  cu.  ft.  per  sec.  and  the  brake  horse-power  = 
36.0,  find  the  efficiency  of  the  pump.     (NOTE.     A  pressure  gage  reads  pres- 
sures above  that  of  the  atmosphere,  a  vacuum  gage  reads  the  amount  by 
which  the  pressure  is  less  than  that  of  the  atmosphere.) 

Ans.  h  =  85.8  ft.,  e  =  81.2  per  cent. 

6.  In  problem  (4)  suppose  that  the  mouth  of  the  pipe  were  66.0  ft.  above 
the  suction  water  level  and  that  the  discharge  were  free  into  the  air. 
Would  the  answers  be  any  different  from  those  in  (4)  ? 


58  CENTRIFUGAL  PUMPS 

7.  Suppose  that  in  the  above  problem  a  nozzle  is  on  the  end  of  the  pipe 
and  the  discharge  is  still  6.0  cu.  ft.  per  sec.     If  the  diameter  of  the  jet  is 
4  in.  and  the  loss  in  the  nozzle  is  0.05F/2/2gr,  where  F3  =  jet  velocity,  solve 
for  head,  pressure  at  (d),  and  water  horse-power  of  the  pump. 

Ans.  h  =  187.2  ft.,  pd  =  174.92  ft.,  127.5  h.p. 

8.  What  is  the  efficiency  of  the  pumping  plant  (including  the  pipe)  in 
(4)  and  (7),  if  the  pump  efficiency  is  70  per  cent,  in  both  cases?     (Take  jet 
velocity  in  (7)  as  useful.) 

Ans.  42  per  cent.,  52.1  per  cent. 

9.  Suppose  that  in  problem  (6)  the  diameter  of  the  pump  impeller  had 
been  1.0  ft.  and  the  speed  1,200  r.p.m.     Would  flow  have  taken  place? 
(b)  How  high  would  water  have  risen  above  the  suction  level?     (c)  What 
would  be  the  reading  on  a  pressure  gage  at  d  if  the  center  of  the  gage  were 
2  ft.  above  the  center  of  the  pipe  or  10  ft.  above  the  suction  level?     (d) 
What  would  be  the  pressure  at  s? 

Ans.  (b)  61.3  ft.     (c)  22.3  Ib.  per  sq.  in.     (d)  p  =   -  6.0  ft.  or  a  vacuum 
of  5.3  in.  of  mercury. 

10.  How  high  must  the  speed  be  in  the  above  problem  to  cause  water  to 
flow  out  of  the  mouth  of  the  pipe? 

11.  If  the  inner  and  outer  radii  of  the  whirlpool  chamber  shown  in  Fig.  1 
are*  6  and  10  in.  respectively,  and  water  leaves  the  impeller  with  a  velocity 
of  70  ft.  per  sec.  at  angle  A2  =  10°,  what  will  be  the  values  of  V,  s,  and  Vr  for 
the  water  leaving  the  whirlpool  chamber?     If  there  were  no  loss  of  energy, 
what  would  be  the  gain  in  pressure? 

12.  If  the  efficiency  of  a  pump  is  75  per  cent,  and  the  thermal  efficiency 
of  a  steam  turbine  driving  it  is  20  per  cent.,  what  is  the  duty  of  the  set? 

13.  If  the  water  horse-power  of  a  pump  is  500  and  the  engine  consumes 
7,000  Ib.  of  steam  per  hr.,  each  pound  of  steam  containing  1,100  B.t.u.,  what 
is  the  duty  of  the  unit? 

Ans.  118,000,000  ft.  Ib. 

14.  If  the  reading  of  the  barometer  is  30  in.  of  mercury,  what  is  the 
pressure  of  the  atmosphere  in  ft.  of  water?     In  Ib.  per  sq.  in.? 

16.  If  a  boiler  requires  3,000  Ib.  of  feed  water  per  hr.  what  must  be  the 
pump  capacity  in  G.P.M.? 

16.  A  pump  discharge  50  cu.  ft.  per  sec.  against  a  head  of  40  ft.     What  is 
the  water  horse-power? 

17.  A  pump  discharges  3,000  G>.M.  against  a  head  of  70  ft.     What  is 
the  water  horse-power? 

18.  A  pump  with  a  6-in.  suction  pipe  is  to  discharge  900  G.P.M.     The 
loss  of  head  at  the  foot  valve  and  entrance  to  the  suction  pipe  is  1.5F2/2gr 
and  the  pipe  friction  factor,  m,  is  0.25.     If  the  minimum  pressure  in  the  suc- 
tion pipe  is  to  be  -  20  ft.,  what  is  the  allowable  height  of  the  pump  above 
the  suction  well? 

Ans.  z  =  14.38  ft. 


CHAPTER  V 


THEORY  OF  CENTRIFUGAL  PUMPS 

35.  Theorem  of  Angular  Momentum.  —  In  Fig.  53  we  will  sup- 
pose a  particle  of  mass  dm  to  be  located  at  a  point  whose  coordi- 
nates are  x  and  y  and  to  be  moving  with  a  velocity  V.  The 
momentum  of  this  particle  will  be  dmV.  The  moment  of  mo- 
mentum is  called  angular  momentum.  For  this  particle  the 
angular  momentum  is  dmV  X  r  cos  A.  Since  the  moment  of  any 
quantity  is  the  algebraic  sum  of  the  moments  of  its  components, 
we  may  write 

dmrV  cos  A  =  dmVyx  —  dmVxy  =  dm 
Differentiating  the  above  we  obtain 

7    d(rVcosA)  (dy    dx  ,       d2y 

dm—    —7.  —        =  dm  l-~  •  -77+  x  - 
dt  \dt      dt  dt 

=  dm(avx  —  axy) 


~  x  —  -77  y  } 


dx 
-j. 

dt 


dy 
-f. 
dt 


—  y 
y 


-3 

dt*/ 


an 

.      I 

i._  _ ____.J,^= 


o  x      o  x 

FIG.  53. 

where  a  denotes  acceleration  with  ax  and  av  as  its  axial  compo- 
nents. (V,  =  dx/dt,  ax  =  dVx/dt  =  d2x/dt2,  etc.).  If  the  re- 
sultant force  acting  on  the  particle  be  denoted  by  dR,  dmay 
=  dRy,  and  dmax  =  dRx.  Thus 

dmd(rV  cos  A)/dt  =  dRyx  -  dRxy 

The  torque  exerted  upon  the  particle  in  Fig.  53  is  seen  to  be 
dR  X  /.     By  the  principle  of  moments 

dR  XI  =  dRyx  -  dRxy 
59 


60  CENTRIFUGAL  PUMPS 

Thus,  if  G  stands  for  torque  so  that  dR  X  I  =  dG, 

dG  =  dmd(rV  cos  A)/dt  (33) 

That  is,  the  time  rate  of  change  of  the  angular  momentum  of  any 
particle  with  respect  to  an  axis  is  equal  to  the  torque  of  the  re- 
sultant force  on  the  particle  with  respect  to  that  axis. 

36.  Torque  Exerted  by  Impeller. — In  Fig.  54  let  us  take  an 
elementary  volume  of  water  as  shown.  If  the  distance  between 
the  web  and  shroud  of  the  impeller  be  denoted  by  b  (ft.),  the  ele- 
mentary mass,  neglecting  vane  thickness,  will  be  if  X  2irrbdr/g. 
Substituting  this  value  of  dm  in  (33)  we  have 

_  w  X  2irrbdr      d(rV  cos  A) 

CL\jf   —  ~~  /\ 


FIG.  54. 

But  dr/dt  =  Vr}  and  2irrb  =  the  area  normal  to  Vr,  so  that 
2irrbdr/dt  =  q.  Since  w  q  =  W 

G  =  —  I    d(rVcosA) 

This  should  be  integrated  between  the  point  where  the  motion 
of  the  water  is  first  influenced  by  the  impeller  and  the  point  where 
the  impeller  ceases  to  act  upon  it.  The  latter  is  usually  taken  as 
(2),  the  point  of  exit,  though  this  may  be  modified  slightly  as 
shown  later.  Since  the  impeller  is  capable  of  exerting  some  effect 
upon  the  water  in  the  eye  and  even  back  in  the  suction  pipe  a  short 
distance,  through  the  medium  of  intervening  particles  of  water, 
we  should  take  the  lower  limit  of  integration  as  the  values  found 
at  (s)  rather  than  (1).  (See  Fig.  1.)  At  (s)  the  water  has .410 


THEORY  OF  CENTRIFUGAL  PUMPS  61 

angular  momentum  about  the  axis.  Therefore  the  torque  ex- 
erted upon  the  water  by  the  impeller  is 

W  W 

G  =  —  r2V2  cos  A 2  =  —  r2s2       .  (34) 

y  y 

If  the  water  flowed  clear  up  to  the  inlet  edge  of  the  impeller 
vanes  without  having  any  rotation  imparted  to  it  we  should  then 
have  A  i  =  90°.  In  such  a  case  the  angular  momentum  at  the 
impeller  entrance  would  be  zero.  In  the  usual  design,  the  im- 
peller angle  a\  is/selected,  so  that  the  flow  at  entrance  will  be  radial 
(i.e.,  AI  =  90°).  But  this  will  not  be  the  case  when  the  discharge 
differs  materially  from  the  normal.  (See  Fig.  56.)  In  such  event 
there  will  be  a  rotation  set  up  in  the  suction  pipe  close  to  the  im- 
peller.1 Thus  the  water,  approaching  along  helical  stream  lines, 
already  possesses  some  angular  momentum  before  it  flows  into  the 
impeller  passages.  But  this  angular  momentum  has  been  derived 
from  the  impeller  and  should  therefore  be  credited  to  it  when 
computing  the  torque. 

In  a  few  cases  centrifugal  pumps  have  been  built  with  guide 
vanes  within  the  eye  of  the  impeller.  Since  the  angle  AI  is  now 
fixed  by  the  form  of  these  guides,  we  should  have  to  write 

G  =  (W/g)(r2s2-rlSl) 

If  the  angle  AI  is  not  90°,  the  value  of  Si  would  not  be  zero.  The 
difference  between  this  case  and  the  preceding  is  that  in  the 
former  the  angular  momentum  of  the  water,  if  any,  at  entrance 
to  the  impeller  is  all  due  to  the  rotating  wheel;  in  the  latter 
case  the  angular  momentum  at  entrance  is 'due  to  the  stationary 
guide  vanes.2 

1  This  has  been  proven  experimentally  by  Clinton  B.  Stewart,  "  Investi- 
gation of  Centrifugal  Pumps,"  Bulletin  of  the  Univ.  of  Wis.,  No.  318,  page 
119.     Readings  were  taken  as  far  as   18  in.  from  the  impeller    but    the 
indications  were  that  the  spiral  vortex  might  "have  extended  for  2  or  3  ft. 

2  This  explanation  is  offered  'because  of  the  common  error  made  by  many 
writers  in  applying  an  equation  for  the  reaction  turbine  to  the  centrifugal 
pump.     For  the  turbine  the  torque  exerted  by  the  water  upon  the  runner 
is  given  by  (W/g)  (nsi  —  r2s2).     When  the  discharge  is  not  radial    (A2  is 
not  90°),  the  second  term  cannot  be  omitted  because  the  angular  momentum 
at  discharge  is  lost  by  the  action  of  other  bodies  than  the  rotating  runner. 
Thus  the  turbine  runner  does  not  absorb  all  the  angular  momentum  of  the 
water;  but  the  pump  impeller,  without  guides  at  entrance,  does  impart  to 
the  water  all  the  angular  momentum  with  which  it  leaves.     The  turbine 


62  CENTRIFUGAL  PUMPS 

The  advantage  of  guide  vanes  within  the  eye  of  the  impeller 
is  that  it  is  possible  to  make  the  angle  A\  less  than  90°  for  the 
normal  rate  of  discharge  without  at  the  same  time  causing  a  heli- 
cal flow  in  the  suction  pipe.  The  latter  is  undesirable  as  the 
water  follows  a  longer  path  and  at  a  higher  velocity  than  in  the 
case  of  a  straight  flow  with  a  resulting  increased  pipe  loss.  The 
advantage  of  making  A\  less  than  90°  is  that  it  requires  a  smaller 
value  of  v-ij  thus  permitting  the  use  of  a  larger  impeller  area  at 
inlet.  For  some  small  capacity  high-speed  pumps  this  may  be 
desirable  as  it  would  materially  decrease  the  friction  losses  within 
the  impeller  passages.  On  the  other  hand,  these  advantages  are 
offset  to  some  extent  by  the  fact  that  the  vanes  introduce  addi- 
tional friction  losses.  Also  when  the  discharge  differs  materially 
from  that  for  which  0,1  is  computed,  there  will  be  a  shock  loss 
similar  to  that  at  the  discharge  from  a  turbine  pump  (Fig.  56). 

37.  Power  Imparted  by  Impeller. — We  may  obtain  an  expres- 
sion for  power  delivered  to  the  water  by  the  impeller  by  multi- 
plying the  torque  (34)  by  the  angular  velocity  «.     Thus,  in  ft. 
Ib.  per  sec., 

Power  =  (TOO  =  (W /g)  (r2s2)  w 

=  (W/g)u*s*  (35) 

This  is  less  than  the  power  required  to  run  the  pump  by  the 
amount  of  the  mechanical  losses  and  greater  than  the  power  de- 
livered in  the  water  by  the  amount  of  the  hydraulic  losses.  Ex- 
pressed in  horse-power  it  would  correspond  to  the  75.0  h.p.  in 
Art.  28.  It  is  analogous  to  the  indicated  power  of  a  reciprocating 
pump. 

38.  Head  Imparted  by  Impeller. — The  power  imparted  to  the 
water  by  the  impeller  may  also  be  represented  by  Wh" '.     Equat- 
ing this  value  to  that  in  (35)  we  have 

Wh"  =  (W/g)(u*d 

From  this  the  head  imparted  to  the  water  by  the  impeller  may 
be  obtained  by  dividing  out  the  W.  Thus 

UtSi     u-2(u2  — 

fi    =  — 

g 

equation  given  can  be  applied,  by  reversing  signs,  only  to  the  centrifugal 
pump  with  guides  at  entrance. 

For  a  pump  without  entrance  guides  it  is  not  correct  to  say  that  nsi 
drops  out  because  the  flow  is  radial,  for  A  i  is  not  necessarily  90°,  at  least  it 
cannot  be  that  for  all  values  of  discharge  for  a  given  pump.  The  term 
riSi  is  eliminated  by  other  considerations. 


THEORY  OF  CENTRIFUGAL  PUMPS 


63 


This  is  not  the  head  actually  developed  by  the  pump.  From 
(36)  must  be  subtracted  the  losses  of  head  to  give  the  actual  head 
developed.  (The  above  corresponds  to  the  60-ft.  head  in  Art. 
28.) 

The  value  represented  by  h"  is  sometimes  called  the  "  theo- 
retical head."  That  does  not  seem  to  be  a  very  desirable  term, 
because  the  quantity  h"  is  a  definite  physical  quantity  in  itself 
and  may  be  determined  by  test  as  well  as  computed  by  theory. 
In  the  same  manner  the  actual  head  h  may  be  either  determined 
by  test  or  computed  by  theory.  But  the  two  terms  represent 
different  things.1  Equation  (36)  does  not  give  a  "  theoretical " 
value  of  the  head  h  for  any  rational  theory  would  also  include 
losses  of  head. 

An  inspection  of  (36)  shows  that  if  a2  =  90°,  the  value  of  h" 
is  independent  of  the  rate  of 
discharge.  If  a2  is  greater 
than  90°,  the  value  of  h" 
will  increase  as  q  increases 
providing  the  pump  speed 
is  constant,  while,  if  «2  is 
less  than  -90°,  the  value  of 
h"  will  decrease.  For  a  con- 
stant speed,  equation  (36)  is  FlG-  55.— Relation  between  q  and  h"  at 
.,  ,.  .  .  '  ,  constant  speed, 

the   equation   of   a  straight 

line.  It  is  often  stated  that  the  three  cases  shown  in  Fig.  55 
for  a2  greater  than  90°,  equal  to  90°,  and  less  than  90°  cor- 
respond to  actual  rising,  flat  or  falling  characteristics  respec- 
tively (Fig.  11).  This  is  due  to  confusing  h"  and  h.  While 
it  is  true  that  pumps  with  a2  greater  than  90°  have  given 
rising  characteristics,  it  is  also  true  that  some  of  them  have 
given  falling  characteristics.  Also  an  angle  of  approximately 
90°  does  not  insure  a  flat  characteristic  as  may  be  seen  in  Fig. 
60.  We  find  that  pumps  with  impeller  angles  of  less  than  90° 
have  also  given  rising  characteristics  as  may  be  seen  in  Fig.  66 
where  a2  =  26°.  The  fact  is  that  the  losses  materially  modify 
the  conditions,  so  that  all  we  can  say  is  that  the  smaller  the  angle 
«2  the  more  tendency  there  is  for  the  head  to  decrease  as  the 
discharge  increases. 

Equation   (36)   is  the  most  convenient  for  numerical  work, 
1  The  difference  may  be  said  to  be  analogous  to  that  between  indicated 
horse-power  and  developed  horse-power. 


64  CENTRIFUGAL  PUMPS 

but  for  some  purposes  another  form  offers  some  advantages. 
We  may  rewrite  (36)  as 

fe»-& 


2, 

From  the  vector  triangle  (Fig.  45)  we  have  that 
TV  =  uz2  —f2u2v2  cos  a2  +  v22 
Inserting  this  value  in  the  above  we  obtain 


The  first  term  may  be  said  to  be  the  pressure  head  imparted 
within  the  impeller,  while  the  second  term  is  the  velocity  head 
that  must  be  converted  in  the  diffuser. 

The  equations  in  this  chapter  apply  directly  to  a  single  impeller. 
For  a  multi-stage  pump  it  is  only  necessary  to  note  that  the  rate 
of  discharge  for  one  impeller  is  common  to  all  of  them,  but  that 
values  of  head  or  power  as  computed  from  the  equations  must  be 
multiplied  by  the  number  of  stages  to  get  the  proper  values  for 
the  entire  pump. 

39.  Losses  of  Head.  —  In  accordance  with  the  usual  method 
in  hydraulics,  the  friction  losses  in  flow  through  the  impeller 
may  be  represented  as  a  function  of  the  square  of  the  velocity. 
The  velocity  concerned  is  the  relative  velocity  and,  since  that 
varies  throughout  the  flow,  we  express  the  loss  in  terms  of  its 
value  at  one  specific  point.  Thus  the  hydraulic  friction  losses 
may  be  represented  by 


where  k  is  an  empirical  factor,  whose  value  can  be  determined 
only  by  experiment. 

If  we  had  guide  vanes  within  the  eye  of  the  impeller,  they 
would  fix  the  value  of  A\.  But  the  values  of  ui,  v\,  and  a^the 
latter  being  a  fixed  impeller  angle,  would  lead  to  the  construction 
of  a  vector  diagram  in  which  the  angle  A\  might  not  necessarily 
agree  with  that  determined  by  the  guides.  There  would  thus 
be  an  abrupt  change  of  velocity  which  would  cause  a  loss  of  head. 
If  no  guide  vanes  were  present,  we  should  still  have  this  loss  if 
the  water  flowed  up  to  the  impeller  without  any  rotation  being 
established  in  it.  But  such  is  not  the  case,  as  has  been  pointed 


THEORY  OF  CENTRIFUGAL  PUMPS 


65 


out  on  page  61.  If  there  is  no  flow,  the  water  in  the  eye  of  the 
impeller  is  set  into  rotation  at  nearly  the  same  angular  velocity 
as  the  impeller.  Thus  for  a  small  rate  of  discharge  it  can  be 
seen  in  Fig.  56,  case  (a),  that  there  is  no  abrupt  change  of  velocity 
as  the  water  flows  into  the  impeller.  As  the  rate  of  discharge 
increases,  this  rotation  in  the  suction  pipe  decreases.  While 
there  is  undoubtedly  some  additional  loss  at  entrance  that  does 
not  follow  the  law  stated  in  (38),  yet  it  does  not  seem  of  sufficient 
magnitude  to  require  a  separate  expression  for  it.  Whatever 
entrance  loss  there  is  may  be  covered  by  a  suitable  value  of  k. 
It  is  hardly  probable  that  k  will  be  constant  in  value. 


FIG.  56. — Velocity  diagrams  and  stream  lines  for  three  rates 
of   discharge. 

Where  the  water  leaves  the  impeller,  however,  there  is  an  im- 
portant loss  which  follows  a  different  law  from  (38).  This  loss 
is  due  to  the  fact  that  there  may  be  an  abrupt  change  of  velocity, 
which  will  result  in  a  violent  turbulent  vortex  motion.  This 
causes  a  large  internal  friction  or  eddy  loss.  To  this  the  term 
" shock  loss"  is  commonly  applied,  though  that  is  not  an  exact 
representation  of  the  actual  phenomenon. 

For  the  turbine  pump  we  may  consider  Fig.  57.  The  diffusion 
vane  angle  A'2  is  fixed  by  construction.  The  values  of  A2  and 
F2  are  determined  by  the  vector  diagram.  If  the  discharge  is  such 
that  v2  =  BD,  then  V2  =  AD  and  A2  =  A'?.  In  this  case  there 
is  no  shock  loss.  But  if  the  discharge  has  any  other  value  such  as 
V2  =  BC',  then  F2  =  AC'  and  A2  is  not  equal  to  A'2.  Therefore 


66  CENTRIFUGAL  PUMPS 

F2,  the  velocity  of  the  water  leaving  the  impeller  at  angle  A2,  will 
be  forced,  as  soon  as  the  water  enters  the  diffusion  vanes,  to 
abruptly  become  F'2(  =  AC)  at  angle  A'2.  The  resultant  loss 
may  be  represented  approximately  by  (CC')2/2g.1  Since  the 
area  of  the  diffusion  ring  normal  to  the  radius  should  equal  the 
area  of  the  impeller  outlet  normal  to  the  radius,  the  radial  com- 
ponent of  F2  should  equal  that  of  V  2.  Therefore  CC'  is  parallel 
to  uz  and  its  value  may  be  found  as  follows:  F'2  sin  A'2  =  v2  sin  a2, 
CCf  =  u-2.  —  F'2  cos  A'  '2  —  Vz  cos  a2.  Substituting  in  the  latter 
the  value  of  F'2  from  the  former  we  get 

sin  a2  cos  A'%  —  vz  cos  a2  sin  A'2)# 


, 

CC       —    Uz   — 


sin  A '2 
sin  (a2  +  A '2 


FIG.  57. 


If  sin((a2  +  A'2)/sin  A'2  =  fc'?the  shock  loss   for  the   turbine 
pump  ma>Tb^T<5ugWy^repr^56nted  by 

(u2  -  Vvtf/Zg  (39) 


With  the  volute  pump  we  have  a  shock  loss  similar  in  its  nature 
to  the  above  for  the  turbine  pump,  but  it  will  be  necessary  to  ex- 
press it  in  different  terms.  Since  the  water  leaving  the  impeller 
with  a  velocity  F2  enters  a  body  of  water  in  the  case  moving  with 
a  velocity  F3  which,  in  general,  is  lower,  we  may,  from  the  analogy 
to  the  pipe  in  Fig.  48(6),  express  the  loss  as  (F2  —  Fa)2/2gf. 
But,  since  these  two  velocities  are  not  in  the  same  straight  line,  it 
will  be  better  to  proceed  as  follows  :  The  velocity  F2  is  resolved 
into  its  components  F2  sin  A2  and  F2  cos  A2.  The  mean  velocity 
in  the  case  F3  is  approximately  parallel  to  F2  cos  A2.  Actually 
there  is  an  angle  between  them  but,  being  small,  it  may  be 
neglected  without  sensible  error.  Great  refinement  is  unwar- 
ranted, since  we  are  unable  to  formulate  a  law  which  will  be 
precisely  correct.  Therefore  we  assume  that  the  radial  component 
of  the  velocity  is  entirely  lost,  while  the  loss  with  the  other  com- 
ponent may  be  represented  by  (F2  cos  A2  —  F3)2/2#.  If  we 

1  L.  M.  Hoskins,  "Hydraulics,"  page  237. 


THEORY  OF  CENTRIFUGAL  PUMPS  67 


write-  F3  =  nv2,  kince  F2  sin  A2  =  v2  sin  a2  and  F2  c*os  A2  =  u2 
-  v  2  cos  a2,  the  shock  loss  for  the  volute  pump  may  be  assumed  to 
be  roughly  given  by1 

(i>2  sina2)2  -f  [uz  -  (n  +  cos 


In  determining  the  value  of  n  for  use  in  (40)  it  would  be  custom- 
ary to  take  it  as  the  ratio  of  fz/F3,  where  F3  is  the  area  of  the 
volute  at  the  section  through  which  all  the  water  passes.  (Or 
if  it  were  taken  as  the  area  at  any  other  section,  a  proportional 
part  of  /2  should  be  taken.)  But  this  value  of  n  would  give  a 
larger  value  for  the  loss  than  is  actually  the  fact.  Instead  of 
every  particle  of  water  in  the  case  flowing  with  a  velocity  deter- 
mined by  q/F3,  it  is  probably  true  that  the  water  near  the  im- 
peller is  moving  with  a  much  higher  velocity  than  this  mean  while 
the  water  adjacent  to  the  outer  boundary  of  the  case  is  moving 
much  slower.  Thus  there  is  no  such  abrupt  change  of  velocity  as 
seems  to  be  implied  by  the  formula.  We  might,  therefore,  mul- 
tiply the  right-hand  member  of  (40)  by  a  factor  less  than  unity  or 
consider  the  F3  that  enters  into  the  formula  as  being  greater  than 
the  mean  velocity.  We  should  thus  accomplish  the  result  by 
making  n  larger  than  the  actual  ratio  of  the  areas.  Experimental 
evidence  is  lacking  as  to  what  this  increase  should  be. 

It  may  be  shown  that  ideally  the  maximum  efficiency  of  con- 
version in  the  volute  is  approximately  attained  when  F3  =  0.5F2, 
the  efficiency  then  being  about  50  per  cent.  It  is  now  thought  to 
be  better  to  make  the  volute  section  smaller  so  that  F3  is  greater 
than  0.5F2  and  to  effect  the  greater  part  of  the  conversion  in  the 
"  nozzle"  shown  in  Fig.  4.  In  fact  in  some  designs  F3  =  F2  cos 
A2  at  the  normal  discharge  so  that  practically  all  of  the  conversion 
is  effected  in  the  nozzle.  Experiments  indicate2  that  the  best 
angle  of  divergence  for  a  circular  passage  is  6°  and  that  the 
loss  of  head  is  0.13(F3  —  Fd)2/2#.  For  other  angles  of  diver- 
gence and  for  non-circular  sections  such  as  are  usual  in  pumps  the 
factor  may  be  increased  to  0.15  or  0.20.  When  the  design  is  such 

1  A  new  method  Is  proposed  by  A.  H.  Gibson  in  "The  Design  of  Volute 
Chambers  for  Centrifugal  Pumps,"  Proc.  of  Inst.  of  Mech.  Eng.,  Apr.,  1913, 
page  519.     While  the  treatment  outlined  gives  much  promise  yet  certain 
objections  must  be  overcome  before  it  can  be  accepted,  as  pointed  out  by 
O.  A.  Price  on  page  550  of  the  same  paper. 

2  Trans.,  Royal  Soc.  of  Edinburgh,  1911,  Vol.  40,  pages  97  and  104. 


68  CENTRIFUGAL  PUMPS 

that  at  normal  discharge  practically  all  the  energy  conversion 
takes  place  in  the  nozzle  rather  than  in  the  volute  proper,  the 
pump  is  said  to  be  analogous  to  a  turbine  pump  but  with  only  one 
diffusion  vane. 

Though  the  expressions  for  shock  loss  for  turbine  and  volute 
pumps  are  unlike  in  appearance,  yet  it  may  be  seen  that  the 
losses  in  each  case  follow  the  same  general  kind  of  law.  As  the 
discharge  of  the  turbine  pump  increases  from  zero,  the  shock 
loss  decreases  until  it  becomes  zero,  then  with  a  further  increase 
in  the  discharge  the  shock  loss  increases  again.  It  may  be  per- 
ceived that  the  right-hand  member  of  (40)  does  likewise.  The 
total  value  of  (40),  however,  never  becomes  zero  as  does  (39), 
but  this  is  of  little  significance.  With  the  turbine  pump  operating 
without  shock  there  is  still  a  failure  to  convert  velocity  head 
into  pressure  head  without  loss,  due  to  the  usual  frictional  re- 
sistance of  the  diffuser  passages  and  the  internal  friction  of  the 
particles  of  water  against  each  other.  But  this  may  be  allowed 
for  by  a  proper  increase  in  the  value  of  k.  Equation  (39)  merely 
expresses  the  portion  of  the  loss  that  is  not  a  simple  function 
of  v22. 

It  must  be  borne  in  mind  that  none  of  these  assumptions  re- 
garding losses  can  be  considered  as  more  than  rough  approxima- 
tions to  the  truth.  There  are  so  many  factors  entering  into  the 
total  losses  that  it  is  not  possible  to  segregate  them  by  ordinary 
experimental  methods.  Attempts  have  been  made  to  compute 
each  separate  item  but  so  many  assumptions  are  required,  and 
it  is  necessary  to  introduce  so  many  unknown  experimental 
factors,  that  it  seems  better  to  the  author  to  combine  all  the 
losses  into  one  term,  save  these  important  shock  losses,  which 
follow  a  different  law  from  the  others.  A  great  deal  of  experi- 
mental work  is  necessary  before  we  can  have  any  truly  rational 
theory,  which  can  be  successfully  applied  in  detail. 

With  either  the  turbine  or  volute  pump  there  is  a  loss  of 
energy  consequent  upon  the  transformation  of  kinetic  energy 
into  pressure,  but  it  is  generally  believed  that  this  operation  can 
be  more  efficiently  performed  with  the  diffusion  vanes.  This  is 
still  open  to  question.  While  it  may  have  been  true  with  the 
older  types  of  pumps,  yet  with  proper  and  careful  design  of 
the  volute  chamber,  it  may  not  be  true.  Since,  with  modern 
pumps,  from  30  to  50  per  cent,  of  the  energy  at  the  point  of  exit 
from  the  impeller  is  kinetic,  it  follows  that  it  is  desirable  to 


THEORY  OF  CENTRIFUGAL  PUMPS  69 

transform  this  as  efficiently  as  possible.  On  account  of  the 
difficulty  of  so  doing  an  effort  is  usually  made  to  keep  the  veloc- 
ity V2  as  low  as  possible.  This  has  led  to  the  use  of  impeller 
vanes  with  a2  less  than  90°  (Fig.  45).  Another  reason  is 
that  it  is  much  easier  to  lay  out  smooth  vanes  with  impeller 
passages  free  from  abrupt  changes  of  area  than  is  the  case  where 
a2  =  90°  or  more.  (Angle  «i  should  always  be  less  than  90°.) 
Both  theory  and  experiment  have  shown  that  better  efficiencies 
may  be  obtained  from  impellers  with  backward  curved  vanes. 

40.  Head  of  Impending  Delivery. — The  head  developed  by 
the  pump  when  no  flow  occurs  is  called  the  "  shut-off  head"  or 
the  "head  of  impending  delivery."  We  are  then  concerned 
only  with  the  "centrifugal  head"  of  Art.  26.  This  was  there 
shown  to  be  equal  to  u22/2g.  The  same  result  may  be  obtained 
from  the  principles  of  Arts.  38  and  39.  In  equation  (36)  if 
Vz  =  Oj,  h"  =  2u22/2g.  The  same  is  true  of  (37)  for  V2  =  u2 
when  v2  =  0.  As  to  the  losses  of  head,  equation  (38)  becomes 
zero  and  by  either  (39)  or  (40),  hf  =  u22/2g,  when  v2  =  0. 
Therefore 

'h  =  h"  -  h' 

=  2u22/2g  -  u22/2g  =  u22/2g  (41) 

The  explanation  of  this  is  that  the  actual  head  imparted  to  the 
water  by  the '  impeller  is  made  up  of  z2  -f-  p2  =  u22/2g  (as  in  Fig. 
51),  and  a  velocity  head  V22/2g  which  is  equal  to  u22/2g  since  the 
velocity  of  a  particle  of  water  at  the  tip  of  the  impeller  blade  is 
u2  if  no  flow  occurs.  Thus  the  actual  amount  of  energy  imparted 
to  the  water  per  pound  is  2u22/2g,  but,  since  there  is  no  oppor- 
tunity to  convert  any  of  this  kinetic  energy  into  pressure,  and 
since  there  is  no  possibility  of  making  use  of  it  otherwise,  the  use- 
ful output  is  only  u22/2g.  That  such  a  loss  does  occur  can  be 
readily  seen,  if  we  suppose  an  infinitesimal  flow  to  occur.  In 
such  event  the  velocity  of  water  outside  the  impeller  would  be 
practically  zero.  Therefore  a  particle  of  water  leaving  the  im- 
peller with  a  velocity  F2  and  entering  this  body  of  water  at  rest 
would  lose  all  of  its  kinetic  energy.  Since  for  such  a  case  V2  =  u2, 
the  proposition  is  evident. 

Although  the  ideal  head  of  impending  delivery  equals  u22/2g, 
we  find  that  various  pumps  give  values  both  above  and  below 
that.  This  may  be  accounted  for  in  a  number  of  ways.  In 
any  real  pump  we  never  have  a  case  of  zero  discharge  through  the 


70  CENTRIFUGAL  PUMPS 

impeller,  for  a  small  amount  of  water  will  be  short  circuited  past 
the  clearance  rings,  through  the  suction  gland  water  seal,  etc. 
This  will  tend  to  make  the  measured  head  greater  or  less  accord- 
ing to  whether  the  pump  has  a  rising  or  a  falling  characteristic. 
With  some  forms  of  cases,  and  especially  where  the  impeller  is 
not  surrounded  by  diffusion  vanes,  there  is  a  tendency  for  the 
water  surrounding  the  impeller  to  be  set  in  rotation.  This 
tends  to  increase  the  head,  since  the  real  effective  value  of  r2 
is  greater  than  the  outer  radius  of  the  impeller.  If  the  water  in 
the  eye  of  the  impeller  is  not  set  in  rotation  at  the  same  angular 
velocity  as  the  impeller  itself,  there  will  be  a  tendency  for  the 
head  to  be  decreased.  This  will  also  be  so  in  case  a  shaft  passes 
through  the  suction  intake,  since  this  will  prevent  the  effective 
value  of  the,  inner  radius  of  the  vortex  from  becoming  zero.  The 
fewer  the  number  of  vanes  and  the  more  the  vanes  are  directed 
backward  the  less  the  head  will  be  because  of  internal  eddies 
that  are  set  up  on  the  rear  of  each  vane  tip.  That  is,  the  water 
surrounding  the  impeller  may  be  said  to  pulsate,  particles  on  the 
front  side  of  each  vane  tip  are  moved  forward  and  outward 
until  they  reach  the  end  of  the  blade,  they  flow  over  this  and  down 
into  the  passage  on  the  rear  of  the  vane.  All  of  these  effects 
together  cause  the  actual  measured  head  for  impending  delivery 
to  depart  somewhat  from  the  value  given  by  (41).  In  rare  cases 
this  departure  is  quite  marked,  but  ordinarily  these  various 
factors  offset  each  other  to  some  extent  so  that  the  discrepancy  is 
not  great. 

It  will  usually  be  found  that  the  actual  head  of  impending 
delivery  is 

h  =  0.85  to  1.10  u22/2g  (42) 

41.  Relation  between  Speed,  Head,  and  Discharge. — When 
flow  occurs,  the  above  relation  no  longer  holds  for  other  factors 
besides  centrifugal  force  become  important.  Due  to  conversion 
of  velocity  head  into  pressure  head,  a  lift  may  be  obtained  which 
is  greater  than  u22/2g.  See  the  " rising  characteristic"  in  Fig. 
11,  page  9. 

The  actual  lift  of  the  pump  may  be  obtained  by  subtracting 
the  losses  In!  from  the  head  imparted  to  the  impeller  h" .  Since 
the  expressions  for  the  losses  of  the  turbine  and  volute  pumps 
are  different,  we  shall  have  to  derive  separate  equations  for 
each.  (See  equations  36,  38,  39,  and  40.) 


THEORY  OF  CENTRIFUGAL  PUMPS  71 


=  h 


For  the  turbine  pump 

2u22  —  2u2v2  cos  a2       kv22       (u2  —  k'v2)2 


2g  2g  2g 

After  rearranging  we  have 

u22  +  2(fc'  -  cos  a2)u2  v2  -  (k  +  fc'W  =  20ft  (43) 

For  the  volute  pump 
2u22  —  2u2v2  cosa2      kv22       fa  sin  a2)2  +  (uz  —  (n  +  cos  a2)v2)2  _  , 

~W~         "W  ~W~ 

After  rearranging  we  have 

u22  +  2nu2v2  -  (n2  +  2n  cos  a2  +  1  +  &>22  =  20ft         (44) 

For  the  sake  of  illustration  it  may  be  useful  to  consider  equa- 
tion (37),  page  64.  If  we  deduct  from  the  left-hand  member 
the  term  k"v22/2g  to  represent  the  losses  within  the  impeller 
passages,  and  multiply  the  right-hand  member  by  m,  a  factor 
less  than  unity,  to  give  the  portion  of  the  velocity  head  that 
is  not  lost,  we  should  have 

u22  -  (1  +  fc>-22  .       TV 

h=     ~^~    ~+mw 

Replacing  F2  in  terms  of  u2  and  vz  and  reducing  we  have 
(1  +  mjuz2  —  2m(cos  a2)u2v2  —  (1  +  kff  —  m)v22  =  2gh 


This  is  easy  to  derive  and  is  easily  explained.  The  disadvantage 
is  that  the  factor  m  varies  between  wide  limits,  being  0  when 
q  =  0  and  ranging  as  high  as  about  0.75  for  the  normal  value  of 
q.  With  equations  (43)  and  (44)  the  factors  are  approximately 
constant  for  a  given  pump. 

These  equations  involve  the  relation  between  the  three 
variables  u2)  v2,  and  h.  If  the  speed  u2  is  constant,  the  rela- 
tion between  v2  and  ft  will  be  the  equation  of  a  parabola.  If 
the  rate  of  discharge  is  constant,  the  curve  between  u2  and  ft 
will  also  be  a  parabola.  If  the  head  ft  is  constant,  either  (43) 
or  (44)  will  become  the  equation  of  a  hyperbola.  Actual  curves 
for  the  three  cases  cited  may  be  seen  in  Figs.  61,  73,  and  74 
respectively.1 

1  The  relation  between  the  three  variables  N,  q,  and  h  may  be  expressed 
by  a  second-degree  equation  of  the  form 

AN2  +  BNq  -  Cq2  -  h  =  0 


72  CENTRIFUGAL  PUMPS 

42.  Use  of  Factors.  —  It  may  be  seen  that  equations  (43) 
and  (44)  involve  ratios  as  well  as  absolute  values.  Thus  we 
might  divide  through  by  2gh  and  we  should  have  equations 
between  the  two  variables  (ui/\/2gh)  and  (v^/^/2gh}.  We 
may  call  these  quantities  <£  and  c  respectively.  Thus 

1*2  =  <l>V2gh  (45) 

v,  =  cV2(jh*  (46) 

The  use  of  these  factors  is  very  convenient  in  many  ways.  Thus 
for  a  given  impeller  we  may  find  the  relations  between  c  and  0 
regardless  of  any  pperating  conditions.  Then  for  any  fixed 
conditions  such  as  either  speed,  discharge,  or  head  the  other 
quantities  may  be  determined.  Thus,  suppose  that  for  a  given 
pump  the  values  for  maximum  efficiency  are  <£  =  1.10  and 
c  =  0.20.  If  the  peripheral  speed  of  the  impeller  is  given,  we 
may  compute  h  from  (45)  and  thus  get  v%  from  (46).  If  the  area 
of  the  impeller  is  known,  the  rate  of  discharge  is  thus  obtained. 
Likewise,  if  the  head  were  specified,  we  could  readily  compute 
the  values  of  u2  and  v2. 

Even  if  definite  values  of  two  of  the  three  variables  are  given, 
the  arithmetic  involved  will  be  found  to  be  simpler  if  equations 
(47)  or  (48)  are  used.  Also  we  can  tell  if  the  computed  factor  0 
or  c  is  unreasonable  far  easier  than  we  could  tell  if  uz,  v2,  or  h  is 
unreasonable.  After  <f>  or  c,  as  the  case  may  be,  is  determined, 
(45)  or  (46)  may  be  employed  to  get  the  quantity  desired. 

Introducing  these  factors  into  (43)  and  (44)  they  become: 
For  the  turbine  pump 

02  +  2(fc'  -  cos  a2)0c  -  (k  +  A/2)c2  =  1  (47) 

For  the  volute  pump 

02  +  2n0c  -  (n*  +  2n  cos  a2  +  1  +  k)c2  =  1          (48) 


where  A,  B,  and  C  are  coefficients.  These  could  be  computed  from  (43) 
or  (44)  by  transforming  into  the  proper  units,  if  the  theory  presented  were 
correct  or  could  be  correctly  interpreted.  Practically  the  three  coefficients 
could  be  obtained  by  inserting  values  of  the  variables  from  three  different 
points  from  an  actual  test  curve.  But,  if  this  method  is  to  have  any  practical 
application  to  design,  numerous  tests  of  all  types  of  impellers  must  be  at 
hand  and  some  means  devised  for  selecting  values  of  A,  B.  and  C  in  terms 
of  the  design. 

*  It  is  useful  in  many  cases  to  note  that  h   =  —  X  I'sri  >  v*  =  (~  )  1*2- 


THEORY  OF  CENTRIFUGAL  PUMPS  73 

From  actual  test  data  it  is  found  that  the  general  range  of 
these  factors,  which  depend  upon  the  design,  is: 
For  impending  delivery 

<t>  =  0.95  to  1.09 
For  maximum  efficiency  (or  rated  discharge) 

c  =  0.10  to  0.30 
0  =  0.90  to  1.30 

43.  Hydraulic  Efficiency.  —  Hydraulic  efficiency  has  been  de- 
nned on  page  55.     That  is 

h       h"       u2(u2  —  v2  cos  a2) 


In  using  this  equation  the  values  inserted  in  it  must  be  either 
determined  by  test  or  computed  from  (43)  or  (44)  as  the  case 
may  be.  (Actually  it  is  better  to  use  (47)  or  (48)  as  noted.) 
If  the  relation  between  these  three  quantities  has  been  determined 
by  test,  it  is  possible  to  compute  the  actual  hydraulic  efficiency 
directly,  if  proper  values  can  be  inserted  in  the  above  expression. 
The  quantity  in  equation  (49)  has  been  termed  "manometric 
efficiency"  or  more  properly  "  manometric  coefficient"  by  many 
writers,  and  treated  as  if  it  were  essentially  different  from  hy- 
draulic efficiency.  Actually  its  numerical  value,  as  h"  is  ordi- 
narily computed  and  with  h  determined  by  test,  may  be  quite 
different  from  what  the  true  hydraulic  efficiency  must  really  be. 
In  some  cases,  for  instance,  its  value  is  less  than  the  gross  ef- 
ficiency, which  is  absurd.  But  this  is  due  to  the  fact  that  the 
theory  is  imperfect  as  pointed  out  in  Art.  48. 

Inserting  the  relations  of  (45)  and  (46)  in  (49),  we  obtain 

eh  =  (50) 


As  in  the  case  above,  this  expression  will  give  the  value  of  the 
hydraulic  efficiency  for  any  conditions  of  operation  provided 
0  and  c  are  simultaneous  values  satisfying  (47)  or  (48). 

44.  Maximum  Hydraulic  Efficiency.  —  The  values  of  <£  and 
c  for  which  the  hydraulic  efficiency  is  a  maximum  may  be  found 
by  applying  the  condition  deh/d<j>  =  0.  The  direct  method  of 
procedure  would  be  to  solve  (47)  or  (48)  for  c  in  terms  of  $ 
and  to  insert  this  value  of  c  in  (50).  We  should  then  have  an 


74  CENTRIFUGAL  PUMPS 

equation  for  efficiency  in  terms  of  0  only,  which  would  be 
differentiated.  The  following  method,  however,  will  be  found 
less  laborious.1  Writing  (50)  as 

1 
7i —  =  0    —  c0  cos  a2 

2eh 

and  differentiating,  we  obtain 

o — 5-  -j—  =  (20  —  c  cos  a2)  —  0  cos  a2  -77  =  0          (51) 

ACfi      (t(b  (t(p 

Differentiating  (47)  and  (48)  we  obtain  respectively 

dc 

[0  +     (kf  -  cos  a2)c]  -  [(k  +  A/2)  c  -  (kf  -  cos  a2)  0]  J^-  =  0 

dc 
(0  +  nc)  +  [w0  —  Cft2  +  2n  cos  a2  +  1  +  ^)cJj,I7=  0 

Equating  values  of  dc/d<j>  given  by  each  of  these  equations  to 
that  given  by  (51),  we  obtain,  if  o:  =  c/0, 
For  the  turbine  pump 

[(k  +  fc'2)  cos  oa]  a2  -  2  (fc  +  /c'2)  a  +  (2fc'  -  cos  o2)  =  0  (52) 
For  the  volute  pump 

[n2  cos  a2  +  2n  cos2  a2  +  (1  +  k)  cos  a2]  a2 

-  2(n2  +  2n  cos  a2  +  1  +  'k)  a  +  (2n  +  cos  o2)  =  0     (53) 

Solving  for  a  from  (52)  or  (53)  we  obtain  the  relation  between 
c  and  0  for  which  the  hydraulic  efficiency  is  a  maximum.  Only 
one  value  of  a,  the  smaller,  will  give  positive  values  of  0.  Since 
c  =  a<f>  for  maximum  efficiency  we  may  substitute  the  latter 
expression  in  place  of  c  in  equations  (47)  or  (48)  and  solve  for  0. 
As  in  any  case,  the  value  of  the  efficiency  may  be  found  by  sub- 
stituting in  (50). 

45.  Maximum  Gross  Efficiency. — The  important  values  of 
0  and  c  are  those  for  which  the  gross  efficiency  is  a  maximum. 
As  may  be  seen  by  an  inspection  of  curves  such  as  those  in  Fig. 
58,  the  maximum  gross  efficiency  will  always  be  obtained  at  a 
higher  rate  of  discharge  than  the  maximum  hydraulic  efficiency. 
This  is  because  of  the  fact  that  the  mechanical  losses  become  of 
smaller  percentage  value  as  the  discharge  increases.  It  is  not 
possible  to  present  a  simple  general  equation  for  the  gross 

1  This  method  of  treatment  for  the  turbine  pump  is  that  given  in  Hoskins 
"Hydraulics,"  page  238. 


THEORY  OF  CENTRIFUGAL  PUMPS  75 

efficiency  which  could  be  treated  as  was  (50),  so  that  no  precise 
formula  can  be  offered  by  which  the  conditions  for  the  maximum 
gross  efficiency  may  be  determined. 

It  is  customary  in  design  to  assume  that  the  shock  loss  is  to 
be  zero  for  the  rated  discharge.  But,  as  may  be  seen  in  Fig. 
58,  the  discharge  for  which  the  shock  loss  is  zero  is  always  greater 
than  that  for  which  the  hydraulic  efficiency  is  a  maximum.  This 
is  due  to  the  fact  that  the  other  hydraulic  friction  losses  become 
of  greater  percentage  value  as  the  discharge  increases. 

If  the  decreasing  percentage  of  the  mechanical  losses  and  the 
increasing  percentage  of  the  other  hydraulic  friction  losses  offset 
each  other,  the  condition  for  zero  shock  loss  may  then  give  the 
maximum  gross  efficiency.  It  will  rarely  be  found  that  these 
two  losses  offset  each  other  exactly,  but  in  view  of  the  imper- 
fection of  the  theory,  this  assumption  may  be  made  as  a  rough 
approximation. 

If  the  shock  loss  is  to  be  zero,  we  should  have  for  the  turbine 
pump  u%  —  k'v?,  =  0,  from  which  </>  =  k'c  or 

sin  A1 '2 

c  =  — — -t ; — TT\$  (54) 

sm(a2  +  A' 2) 

With  the  volute  pump  we  shall  equate  the  right-hand  member  of 
(40)  to  zero.  Thus  <j>  —  (n  +  cos  a2)  c  =  0  or 

c  =  -  (55) 

n  -f-  cos  «2 

To  find  the  condition  for  which  the  shock  loss  is  zero  with  the 
turbine  pump  we  may  substitute  the  value  of  c  given  by  (54) 
in  (47)  and  solve  for  <f>.  For  the  volute  pump  we  may  sub- 
stitute the  value  of  c  given  by  (55)  in  (48)  and  solve  for  0. 

46.  Experimental  Analysis. — In  order  to  illustrate  the  pre- 
ceding theory,  an  analysis  has  been  made  of  two  pumps  tested 
by  the  author  and  for  which  all  essential  dimensions  were  ob- 
tainable.1 Curves  for  a  turbine  pump  are  shown  in  Fig.  58 
and  for  a  volute  pump  in  Fig.  59.  The  test  data  gave  directly 
for  all  rates  of  discharge  the  head  developed,  the  brake  horse- 
power, the  water  horse-power,  and  the  gross  efficiency.  For  the 
turbine  pump  the  bearing  friction  was  also  determined  by  test. 
The  disk  friction  was  estimated  from  the  formulas  presented  in 

1  Illustrations  of  these  pumps  may  be  seen  in  Figs.  62,  63,  64,  and  65. 
The  test  data  is  recorded  in  Appendix  A. 


76 


CENTRIFUGAL  PUMPS 


Chap.  VII,  and  a  reasonable  leakage  loss  was  assumed.  The  re- 
mainder of  the  power  lost  was  held  to  be  due  to  hydraulic  friction 
losses.  However,  for  small  rates  of  discharge  there  is  another 
source  of  loss  which,  for  want  of  a  better  name,  has  been  termed 
"churning  loss."  This  loss  is  due  to  eddies  set  up  in  the  water  sur- 


0  0.1  0.2  0.3  0.4  0.5  0.6 

Discharge-Cu.  Ft.  per  Second 

FIG.  58. — Analysis  of  2-stage  Worthington  turbine  pump  at  constant  speed. 

rounding  the  periphery  of  the  impeller.1  This  loss  is  the  greatest 
at  zero  discharge,  but,  as  the  flow  is  increased,  it  diminishes  and 
finally  ceases  when  the  discharge  is  great  enough  to  cause  the 
water  to  flow  smoothly  away  from  the  impeller.  This  loss  of 
power  is  similar  to  disk  friction  but  it  has  not  been  classed  as  a 

1  R.  Biel,  Mitteilungen  iiber  Forschungsarbeiten,  Heft  42. 


THEORY  OF  CENTRIFUGAL  PUMPS 


77 


mechanical  loss,  as  disk  friction  has  been,  because  it  is  a  function 
of  the  discharge  and  also  affects  the  head  developed.  Neither 
has  it  been  classed  as  a  pure  hydraulic  loss  because,  though  it 
affects  the  head  as  noted  on  page  70,  it  is  not  strictly  a  function 
of  head  as  other  hydraulic  losses  are.  If  it  were  a  function  of 


/ 


0.2      0.4      0.6 


0.8      1.0      1.2      1.4      1.6      1.8      2.0      2.2      2.4 

Discharge-Cu.  ft.  per  Second 


2.6 


FIG.  59. — Analysis  of  single-stage  De  Laval  centrifugal  pump  at  constant 

speed. 

head,  the  loss  of  power  would  be  zero  when  q  is  zero,  since  power 
lost  equals  wqh'.  It  has,  therefore,  been  left  as  a  separate  item. 
That  there  is  some  such  additional  loss  of  power  for  small  dis- 
charges must  be  evident  from  an  inspection  of  test  data  from 
many  pumps.  For  instance  in  Fig.  59  it  is  seen  that  at  zero 
discharge  the  brake  horse-power  is  greater  than  the  total  loss 


78  CENTRIFUGAL  PUMPS 

of  power  (b.h.p.  —  w.h.p.)  at  normal  discharge.  Since  the  usual 
mechanical  losses  do  not  vary  appreciably  with  the  discharge,1 
while  the  hydraulic  losses  increase  from  zero,  it  is  seen  that  the 
brake  horse-power  at  shut-off  should  be  less  than  the  (b.h.p.  - 
w.h.p.)  at  any  rate  of  discharge,  unless  there  were  some  other 
items. 

Although  these  curves  involve  assumptions  and  approxima- 
tions, they  still  show  very  accurately  the  relative  relations  be- 
tween various  losses.  The  author  believes  also  that  the  absolute 
numerical  values  cannot  be  very  much  in  error.  Assuming  that 
they  are  correct,  we  can  then  compute  the  actual  hydraulic 
efficiency  as  equal  to  w.h.p./(w.h.p.  +  hyd.  losses).  It  is  seen  that 
for  zero  discharge  the  hydraulic  efficiency  does  not  become  zero, 
as  might  be  expected.  The  reason  is  that,  as  the  discharge  be- 
comes smaller  and  smaller,  the  values  in  both  numerator  and 
denominator  of  the  above  expression  approach  zero.  Therefore 
at  zero  discharge  the  hydraulic  efficiency  is  0/0.  This  may  be 
evaluated  by  noting  that  (w.h.p.  +  hyd.  losses)  =  wqh"/55Q. 
Thus  €h  =  wqh/wqh"  =  h/h".  It  is  seen  that  the  hydraulic 
efficiency  may  have  some  finite  value  even  though  q  is  zero. 
From  a  consideration  of  Art.  40  we  should  expect  the  hydraulic 
efficiency  for  impending  delivery  to  be  50  per  cent.  Actually 
it  may  differ  slightly  from  this  due  to  the  fact  that  we  have  a 
small  amount  of  leakage  water  that  circulates  through  the 
impeller.  Even  when  the  power  output  is  zero,  a  finite  value  of 
the  hydraulic  efficiency  is  reasonable  if  we  regard  the  mere 
development  of  pressure  as  being  a  useful  result. 

If  we  divide  the  actual  head  developed,  h,  by  the  actual  hy- 
draulic efficiency,  we  obtain  the  actual  value  of  h",  the  head  im- 
parted by  the  impeller.  This  is  seen  to  differ  from  the  curve 
for  h"  as  computed  by  the  ordinary  methods.  The  reasons  for 
this  discrepancy  will  be  discussed  in  Art.  48. 

Subtracting  values  of  h  from  h"  we  obtain  values  of  h',  the 
head  lost  in  friction  losses  within  the  impeller  and  diffusion  vanes 
or  volute.  With  our  present  experimental  knowledge  any  sub- 

1  If  the  bearing  friction  losses  varied  at  all  they  would  increase  with  the 
discharge  due  to  greater  end  thrust.  The  leakage  losses  will  decrease  as 
the  discharge  increases,  but  not  as  much  as  might  be  thought.  As  the  flow 
is  increased  not  only  does  the  pressure  at  discharge  decrease  but  the  suction 
pressure  likewise  diminishes.  The  leakage  is  a  function  of  the  difference 
between  these  two,  and  that  difference  does  not  decrease  as  rapidly  as  does  h. 


THEORY  OF  CENTRIFUGAL  PUMPS  79 

division  of  hf  is  a  matter  of  conjecture.  For  the  turbine  pump 
in  Fig.  58,  the  shock  loss  was  computed  by  (39)  and  the  rest  of 
the  loss  taken  to  be  the  remaining  hydraulic  losses.  It  may  be 
seen  that  this  curve  does  not  represent  a  loss  which  varies  as 
i>22  as  assumed  in  (38).  This  may  be  due  to  the  fact  that  (39) 
is  not  an  exact  representation  of  the  law  by  which  the  shock 
loss  varies.  Again  the  "  churning  loss"  may  not  have  been  cor- 
rectly assumed,  thus  affecting  the  value  of  6k,  h,  and  h'  for  the 
smaller  discharges.  Also  it  is  highly  probable  that  there  are 
various  minor  losses  which  do  not  follow  precisely  the  law 
stated  in  (38).  But  in  the  main  the  curves  shown  represent  the 
general  appearance  of  the  true  curves  at  least. 

47.  Effect  of  Number  of  Vanes. — It  is  necessary  to  have  a 
certain  number  of  vanes  in  an  impeller,  otherwise  proper  guidance 
of  the  water  will  not  be  obtained.     On  the  other  hand  too  many 
vanes  will  cause  too  much  frictional  resistance  to  flow.     But 
for  a  reasonable  number  of  vanes  the  effect  upon  the  efficiency 
is  slight.     This  may  be  seen  by  the  curves  in  Fig.  60,  where  the 
number  of  vanes  was  varied  from  six  to  twenty-four  but  without 
other  material  changes  being  made.1     It  cannot  be  argued  from 
these  curves  that  the  efficiency  increases  as  the  number  of  vanes 
decreases,  because  with  another  series  having  different  types  of 
vanes  the  lowest  efficiency  was  obtained  with  six  vanes.     But  it 
can  certainly  be  said  that  the  difference  is  not  material. 

The  efficiencies  shown  by  these  curves  are  low  but  that  is  be- 
cause the  impellers  were  constructed  for  experimental  purposes 
and  not  to  give  high  efficiencies.  Also  the  case  was  very  poor. 
Substitution  later  of  a  good  spiral  case  added  31  per  cent,  to  the 
efficiency  of  the  same  impeller. 

For  the  three  impellers  with  different  numbers  of  vanes  the 
relation  between  head  and  discharge  varied  slightly  as  may  be 
seen  and  the  maximum  efficiency  was  obtained  at  different  rates 
of  discharge.  A  general  conclusion  might  be  that  the  fewer  the 
number  of  vanes  the  lower  the  normal  head  and  the  larger  the 
normal  discharge. 

48.  Defects  of  the  Theory. — The  defects  of  this  theory  or 
any  hydraulic  theory  are  as  follows:  In  order  to  apply  simple 
mathematics  to  the  problem,  it  is  necessary  to  idealize  the  con- 
ditions of  flow  by  assuming  that  all  particles  of  water  move  in 

Clinton  B.  Stewart,  "Investigation  of  Centrifugal  Pumps,"  Bulletin 
of  the  Univ.  of  Wis.,  No.  173,  page  529. 


80 


CENTRIFUGAL  PUMPS 


similar  paths  with  equal  velocities  and  angles.  We  know  that 
this  is  not  in  accordance  with  actual  facts,  but  to  undertake 
to  analyze  the  motions  of  all  the  particles  would  be  beyond  our 


o  i.o 

Discharge  in  Cu.Ft.  per  Second 

FIG.  60. — Effects  of  different  numbers  of  vanes. 

present  ability.     Thus  our  equations  deal  merely  with  average 
values  of  velocities  and  angles.     This  is  incorrect  in  principle 


THEORY  OF  CENTRIFUGAL  PUMPS  81 

as  may  readily  be  shown  by  the  following  numerical  illustra- 
tion. Suppose  we  have  bodies  of  equal  mass  m,  one  of  which 
moves  with  a  velocity  of  10  ft.  per  sec.  and  the  other  is  at  rest. 
It  is  clear  that  the  true  kinetic  energy  of  the  system  is  m  X  102/2 
+  0  =  50m.  The  average  velocity  of  the  two  bodies  is  5  ft.  per 
sec.  and  the  kinetic  energy  computed  on  that  basis  is  (m  +  m) 
52/2  =  25w.  This  is  half  of  the  true  value. 

But  even  to  determine  the  average  values  that  should  be  used 
in  the  equations  is  often  a  matter  of  difficulty.  -Thus,  though 
the  direction  of  the  streams  leaving  thfi  impeller  is  influenced 
by  the  vane  angle  at  that  point,  it  cannot  be  said  that  the  angle 
a2  is  exactly  equal  to  the  vane  angle.  In  fact  the  writer  has 
provelTby  some  investigations  that  the  two  may  differ 


by  from  5  to  10°  and  that  a2  furthermore  varies  with  </>  and  is 
not  a  constant  quantity.  The  same  may  be  said  of  the  area  /2. 
Experiments  have  indicated  that  there  may  be  a  certain  amount 
of  contraction  of  the  streams  leaving  a  reaction  turbine  runner 
and  that  this  contraction  varies  with  conditions.1  Thus  the 
true  value  of  /2  may  really  be  less  than  the  area  of  the  impeller 
passages.  These  same  observations  may  be  extended  to  all  the 
angles  and  areas  that  enter  into  the  theory.  The  theory  deals 
with  stream  lines,  but  we  have  to  use  in  it  values  that  we  obtain 
from  the  construction. 

Aside  from  these  considerations,  it  must  be  realized  that  we 
have  yet  no  absolutely  correct  expressions  for  the  various  losses 
that  affect  the  head  developed. 

The  fact  that  there  is  a  discrepancy  between  the  ordinary 
theory  and  the  actual  facts  may  be  seen  in  Figs.  58  and  59.  The 
actual  values  of  In"  were  determined  from  test  data.  While 
there  is  some  uncertainty  about  the  exact  values,  yet  the  curves 
shown  cannot  be  very  much  in  error.  The  ideal  values  of  h" 
were  computed  from  the  theory  that  has  been  presented,  due 
allowance  being  made  for  the  flow  through  the  impeller  of  the 
leakage  water.  The  difference  between  these  two  values  of  h" 
is  the  cause  of  the  difference  between  true  hydraulic  efficiency 
and  "manometric  coefficient." 

It  is  found  that  the  greater  the  number  of  vanes  the  better 
does  the  theory  agree  with  the  facts,  the  reason  for  this  being 
that  the  actual  stream  lines  are  compelled  to  conform  more 
closely  to  the  impeller  passages.  Thus  the  values  used  in  the 

1  Zeit.  des  Vereins  deut.  Ing.,  May  13,  1911. 


82  CENTRIFUGAL  PUMPS 

theory  are  more  nearly  the  true  values  than  otherwise.  But  a 
wide  departure  from  the  computed  results  does  not  mean  a  loss 
of  efficiency,  necessarily,  as  has  just  been  shown  in  the  preceding 
article. 

49.  A  Corrected  Theory. — Bearing  in  mind  the  reasons  for 
the  defects  of  the  ordinary  theory,  an  attempt  will  be  made  to 
present  several  ways  of  meeting  the  difficulty. 

Equation  (35)  shows  that  the  power  imparted  to  the  water  by 
the  impeller  is.  (W/g)  u2s2.  But,  as  has  been  pointed  out,  this 
can  be  true  only  if  all  particles  of  water  move  exactly  alike. 
However  this  equation  may  be  applied  to  an  infinitesimal  mass 
of  water  discharging  from  the  impeller  so  that 

d(Wh")  =  dWu2s2/g 

Let  dF  represent  an  element  of  area  normal  to  the  radial  com- 
ponent of  velocity  at  discharge  from  the  impeller.  Then 
dW  =  wV2  sin  A2dF  and,  since  s2  =  V2  cos  A2) 

Wh"  =  (wu2/g)fV22  sin  A2  cos  A2dF 

=  (wu2/2g)  f  F22  sin  2 A  2dF  (56) 

If  V2  and  A2  are  constant,  as  ordinarily  assumed,  this  expression 
may  readily  be  integrated  and  becomes  equation  (35).  But  it 
is  certain  that  V2  and  A2  are  not  constant.  They  will  undoubt- 
edly be  found  to  vary  across  the  section  of  every  stream  dis- 
charged from  each  impeller  passage.  Also  it  is  known  that 
with  some  cases,  at  least,  unequal  amounts  of  water  are  dis- 
charged around  different  portions  of  the  circumference.  If  it 
were  known  how  V2  and  A2  varied,  so  that  (56)  could  be  inte- 
grated, it  is  believed  that  a  true  value  could  be  obtained  for  the 
power  imparted  to  the  water  by  the  impeller.1 .. 

In  order  to  evaluate  (56)  we  might  represent  dF  as  r2dOdb, 
where  r2d&  is  a  portion  of  the  arc  of  the  circumference  and  db  is  a 
length  parallel  to  the  axis  or  shaft.  It  would  then  be  necessary 
to  be  able  to  express  V2  and  A2  as  functions  both  of  0  and  b. 

Lacking  the  knowledge  that  would  enable  us  to  integrate  (56), 
we  must  fall  backjipon  empirical  methods.  One  method  would 
be  to  multiply  s2  by  some  empirical  factor.  This  factor  can  be 
determined  only  by  experience  and  would  probably  depend  upon 

1  This  is  practically  the  same  method  given  by  C.  B.  Stewart  in  Bulletin 
of  the  Univ.  of  Wis.,  No.  173,  page  551. 

For  a  different  discussion  see  "Neue  Theorie  und  Berechung  der  Kreisel- 
rader"  by  H.  Lorenz. 


THEORY  OF  CENTRIFUGAL  PUMPS  83 

the  vane  angle  and  the  number  of  vanes.  With  a  given  impeller 
it  would  also  vary  with  the  rate  of  discharge.  In  Figs.  58  and 
59  it  is  the  ratio  of  the  actual  h"  to  the  ideal  h".  In  order  to 
obtain  the  actual  head  developed  we  could  then'  subtract  com- 
puted values  of  In!  from  the  h"  computed  with  our  empirical 
factor,  or  we  could  multiply  the  latter  by  a  hydraulic  efficiency 
which  experience  would  lead  us  to  choose.  (It  may  be  seen  that 
h  =  eh  X  h"  (actual).  But  h"  (actual)  =  empirical  factor  X  h" 
(ideal).  Therefore  h  =  eh  X  empirical  factor  X  h"  (ideal).  Thus 
the  "manometric  coefficient"  is  the  product  of  the  actual  hy- 
draulic efficiency  times  this  empirical  factor.) 

Instead  of  considering  the  water  discharging  across  the  arc 
AB  in  Fig.  46,  we  may  consider  it  at  discharge  across  the  line 
AC  and  base  our  computations  upon  the  values  there  encountered. 
Since  it  is  clea'r  that  the  peripheral  velocity  varies  from  A  to  C, 
we  shall  take  the  mean  point  M  and  use  the  values  of  u%  and  s2 
as  obtained  for  M  in  equation  (36).  The  only  logical  reason 
that  may  be  advanced  for  this  procedure  is  that  the  water  is  no 
longer  confined  between  the  two  vanes  after  it  crosses  line  AC. 
But  it  would  seem  as  if  the  water  flowing  from  C  to  B  would 
still  be  receiving  energy  from  the  vane,  and  there  are  many  other 
reasons  against  this  as  being  a  logical  mathematical  procedure. 
However,  it  has  been  shown  that  the  value  of  h",  as  ordinarily 
computed,  is  too  high  and  .that  the  fewer  the  number  of  vanes 
the  greater  the  excess  over  the  true  value.  It  is  seen  that  basing 
computations  upon  the  point  M  will  give  smaller  values  of  h" 
and  that  the  fewer  the  number  of  vanes  the  greater  this  reduction 
will  be.  But  this  method  can  be  employed  only  when  water  is 
being  delivered.  Computations  for  shut-off  must  be  based  upon 
the  outer  impeller  diameter,  and  for  very  small  discharges  the 
true  value  of  h"  will  be  intermediate  between  that  given  by  either 
method  of  computation.  By  trying  this  method  out  with 
several  pumps  that  differed  materially  from  each  other,  the 
author  has  found  that  at  normal  discharge  the  computed  h" 
would  agree  within  a  few  per  cent,  of  the  value  determined  from 
test  results.  But  he  would  attribute  this  close  agreement  to  a 
coincidence  rather  than  to  a  logical  mathematical  relation.  But, 
since  this  does  offer  an  empirical  method  of  correction  that  is  in 
the  right  direction  and  since  it  so  often  fits  the  actual  facts,  it 
may  be  employed  to  give  values  of  h"  that  will  be  approximately 
true. 


84  CENTRIFUGAL  PUMPS 

50.  Value  of  the  Theory. — Although  the  ordinary  theory, 
without  empirical  modification,  is  admittedly  defective,  it  is 
nevertheless  of  great  value.  While  we  may  be  unable  to  compute 
correct  numerical  values  by  it,  it  still  serves  to  indicate  relative 
values.  If  from  tests  we  know  what  the  actual  results  are, 
the  theory  will  enable  us  to  predict  the  effect  of  changing  various 
dimensions.  Thus  the  theory  indicates  that  the  smaller  the 
vane  angle  a2  the  steeper  the  characteristic  will  be.  If  we 
know  the  actual  value  of  the  head  developed  by  an  impeller 
with  a  certain  vane  angle,  we  can  estimate  the  reduction  of  head 
caused  by  a  smaller  angle  or  the  amount  of  increase  produced 
by  a  larger  angle.  But  theory  must  always  work  hand  in  hand 
with  experience,  as  the  number  of  vanes  also  affects  the  head. 
The  theory  does  not  involve  this  factor. 

The  theory  is  also  very  useful  in  explaining  the  actual  char- 
acteristics obtained  from  centrifugal  pumps  and  to  enable  us 
to  understand  the  principles  involved  in  their  design.  A  ra- 
tional theory  in  conjunction  with  tests  will  facilitate  the  devel- 
opment of  new  designs. 

In  order  to  see  the  application  of  theory  to  the  general  problem 
of  design,  let  us  consider  the  angles  a2  and  A'2  for  the  turbine 
pump.  (A  similar  discussion  would  apply  to  the  volute  pump.) 
From  equation  (36)  it  might  appear  that  it  would  be  desirable 
to  make  the  angle  a2  about  90^  or  even  greater,  as  a  highej 
head  would  be  developed  "with  a^given  pump  speed.  The 
undesirable  feature  of  this  is  that  it  would  result  in  a  higher 
absolute  velocity  at  exit  from  the  impeller.  (See  Fig.  45.) 
The  difficulty  of  transforming  this  velocity  head  into  pressure 
is  such  as  to  make  the  resulting  efficiency  lower.  In  addition 
it  is  difficult  to  construct  vanes  with  the  proper  curvature  if 
q2_is  too  large.  But  it  is  not  desirable  to  make  a2  too  small 
either  because  it  would  be  necessary  to  run  the  impeller  at  a 
hipher^ajiged  to  Develop  a  given  head  than  would  be  the  case 
otEerwiseT  The  additional  disk  friction  losses  would  offset 
the  increased  hydraulic  efficiency.  Also  the  smaller  the  angle 
a2  the  smaller  the  area  of  the  impeller  passages  as  may  be  seen 
from  equation  (4).  This  would  imply  a  very  small  capacity 
for  a  given  size  of  impeller,  if  the  vane  angle  is  not  given  a 
reasonably  large  value.  And  a  small  capacity  pump  would 
have  a  low  efficiency  because  of  the  greater  percentage  value 
of  the  mechanical  losses.  Values  of  the  vane  angle  cr2  niay  be 


THEORY  OF  CENTRIFUGAL  PUMPS  85 

as  small  as  10°  in  some  cases  and  as  large  as  80°  in  some  in- 
stances but  the  more  usual  values  are  from  20°  to  30°. 

By  an  inspection  of  Fig.  57,  it  may  be  seen  that  the  smaller 
the  diffusion  vane  angle_J4/2_the  smaller  the  rate  of  discharge 
at  which  the  shock  loss  becomes  zero.  From  the  curves  in  Fig. 
58,  it  is  clear  that  the  minimum  value  of  the  total  hydraulic 
losses  is  less  for  such  a  case  and  that  the  minimum  value  will  be 
found  at  a  smaller  discharge.  Thus  the  smaller  the  angle  A'2 
the  higher  thehy^muh^eJS^iejicy  will  be,  but  the  smaller  the 
rate 'oTdischarge  at  which  it  is  found.  (This  may  also  be  shown 
by  the  extractions  but  not  so  clearly  as  by  the  curves.)  Therefore 
as  A' 2  approaches  zero,  h'  approaches  zero,  q  approaches  zero, 
while  the  maximum  hydraulic  efficiency  approaches  100  per 
cent.  But  an  angle  of  0°  with  a  zero  discharge  Would  be 
absurd.  In  order  to  secure  a  reasonable  rate  of  discharge 
from  a  given  impeller  it  is  desirable  to  sacrifice  hydraulic  efficiency 
to  some  extent  by  increasing  the  value  given  A'2.  But  this 
does  not  really  mean  a  sacrifice  of.  gross  efficiency,  which  is  the 
important  practical  quantity.  In  the  imaginary  case  of  A'2  =  0°, 
we  find  that  eh  =  100  per  cent.  But,  since  the  water  power  out- 
put would  be  zero,  the  gross  efficiency  would  be  zero.  Thus  for  a 
series  of  pumps  alike  in  every  respect  except  that  of  the  diffusion 
vane  angle,  we  should  find  that  as  A'2  increased  the  maximum 
hydraulic  efficiency  would  decrease.  But  since  this  rrfaximum 
would  be  found  at  higher  rates  of  discharge,  the  water-power 
output  would  be  greater  and  this  would  be  conducive  to  a 
higher  mechanical  and  volumetric  efficiency.  The  gross  effi- 
ciency being  the  product  of  a  decreasing  hydraulic  efficiency  and 
an  increasing  mechanical  and  volumetric  efficiency  would  at 
first  increase  asA'2  increased  from  zero,  and  then  later  decrease 
as  the  hydraulic  efficiency  became  the  more  decisive  factor.  It 
is  desirable  that  such  values  ofjl^be  used  as  will  lead  to  the 
maximum  gross  efficiency  being  attained.1  This  can  be  deter- 
mined solely  by  experiment.  It  is  customary  to  make  A\  from 
5°  to  10°  for  high- head  pumps  and  to  use  values  up  to  about  30° 
in  some  cases  of  low-head  turbine  pumps. 

1  The  maximum  efficiency  of  a  series  of  pumps  such  as  here  considered  must 
be  clearly  distinguished  from  the  maximum  efficiency  of  a  single  pump  with 
values  of  a2  and  A'2  fixed.  The  latter  case  is  treated  in  Arts.  44  and  45. 


86  CENTRIFUGAL  PUMPS 


51.  PROBLEMS 

1.  The  diameter  of  a  centrifugal  pump  impeller  is  20  in.,  the  value  of  <£ 
is  1.053,  and  the  head  required  is  240  ft.     (a)  If  it  is  a  single-stage  pump, 
what  is  the  necessary  rotative  speed?     (b)  What  is  the  necessary  speed  for 
a  4-stage  pump? 

Ans.  (a)  1,500  r.p.m.,  (b)  750  r.p.m. 

2.  The  diameter  of  a  pump  impeller  is  6  in.,  the  speed  is  3,000  r.p.m.. 
and  the  value  of  <f>  is  1.093.     (a)  What  will  be  the  head  developed  by  a  single- 
stage  pump?     (b)  What  will  be  the  head  developed  by  a  3-stage  pump? 

Ans.  (a)  80  ft.,  (b)  240  ft. 

3.  For  a  turbine  pump  a2  =  15°,  A'2  =  7°,  k  =  4.0  (assumed),  r2  =  0.50 
ft.,   TI  =  0.25  ft.,  /2  =  0.20  sq.  ft.,  fl  =  0.18   sq.   ft.     For  the  maximum 
hydraulic  efficiency  find  <f>,  c,  and  eh. 

Ans.  a.  =  0.215,  <f>  =  0.883,  c  =  0.19,  eh  =  0.808. 

4.  If  c  =  0.25,  find  <f>  for  the  pump  in  (3). 
Ans.  0  =  0.929. 

5.  If  <f>  =  1.00,  find  values  of  c  for  the  pump  in  (3). 
Ans.  c  =  0,  and  0.312. 

6.  Find  values  of  <j>  and  c  for  zero  shock  loss  for  the  pump  in  (3). 
Ans.  <f>  =  1.030,  c  =  0.336. 

7.  When  the  shock  loss  at  exit  is  zero,  what  must  be  the  vane  angle  with 
the  pump  in  (3)  for  the  absolute  flow  at  entrance  to  be  radial? 

Ans.  ai  =  47.6°. 

8.  For  the  case  in  problem  (6)  find  the  r.p.m.  and  the  rate  of  discharge 
if  the  head  is  100  ft. 

Ans.  1,580  r.p.m.,  5.40  cu.  ft.  per  sec. 

9.  Plot  curves  between  head  and  hydraulic  efficiency  as  ordinates  against 
values  of  discharge  as  abscissae  for  the  pump  in  problem  (3)  running  at  a 
constant  speed  of  1,700  r.p.m. 

10.  For  a  volute  pump  a2  =  15°,  k  =  5.0  (assumed),  n  =  2.0.     For  the 
maximum  hydraulic  efficiency,  find  values  of  <£,  c,  and  €h 

Ans.  a.  =  0.198,  0  =  0.894,  c  =  0.177,  eh  =  0.755. 

11.  For  the  pump  in  (10)  with  r2  =  0.30  ft.  and  /2  =  0.25  sq.  ft.  plot 
curves  of  head  and  hydraulic  efficiency  against  discharge  for  a  constant  speed 
of  1,200  r.p.m. 

12.  Compute  the  coefficients  A,  5,  and  C  for  the  equation  in  the  footnote 
on  page  71,  from  the  curves  in  Figs.  58  and  59. 

13.  Compute  the  coefficients  A,  B,  and  C  from  the  theory,  using  the  di- 
mensions given  in  Art.  53.     Compare  with  the  results  in  problem  (12). 

14.  For  a  centrifugal  pump  running  at  1,500  r.p.m.,  h  =  90  ft.,  when 
q  =  1.5  cu.  ft.  per  sec.     If  r2  =  0.50  ft.,  «2  =  30°,  and  /2  =  0.10  sq.  ft., 
find  the  "manometric  coefficient."     (b)  If  the  actual  hydraulic  efficiency  is 
0.850,  what  is  the  value  of  the  " empirical  factor"  of  Art.  50? 

Ans.  (a)  0.563,  (b)  0.663. 

15.  Compute  the  "manometric  coefficients"  from  the  curves  in  Figs. 
58  and  59,  at  discharges  of  0.425  and  1.30  cu.  ft.  per  sec.  respectively. 

16.  Compute  the  " empirical  factors"  of  Art.   50  from  the  curves  in 
Figs.  58  and  59. 


THEORY  OF  CENTRIFUGAL  PUMPS  87 

17.  For  a  turbine  pump  the  vane  angle  at  exit  =  30°,  and  the  diffusion 
vane  angle  =  7°.     If  k  =  4.0  and  c  =  0.15,  find  ideal  values  of  </>  and  eh. 
(b)  If  the  actual  value  of  <£  is  1.00,  find  true  value  of  c,  manometric  coefficient, 
and  the  "empirical  factor." 

Solution:  (a)  By  (47)  <£  =  0.852  and  by  (50)  eh  =  0.813.  (b)  From  (45) 
and  (46)  it  is  seen  that  uz/v2  =  <t>/c.  We  are  assuming  that  the  values  of 
uz  and  t»2  are  fixed  and  that  h  is  the  uncertain  element  in  the  theory.  There- 
fore, if  the  true  value  of  <£  is  1.00  rather  than  0.852,  the  value  of  c  must  be 
increased  in  the  same  proportion,  since  the  ratio  of  </>/c  is  constant.  Thus 
the  true  value  of  c  is  (1.00/0.852)  X  0.15  =  0.176.  Introducing  0  =  1.00 
and  c  =  0.176  in  (50),  we  get  eh  =  0.590.  This  is  the  "manometric  coeffi- 
cient" and  is  less  than  the  true  hydraulic  efficiency,  because  it  is  based  upon 
actual  values  of  <£  and  c  rather  than  ideal  values.  The  true  hydraulic 
efficiency  may  be  taken  as  the  value  determined  in  (a).  Therefore  the 
"empirical  factor"  is  0.590/0.813  =  0.725.  This  treatment  assumes  that 
the  actual  value  of  h  is  the  same  per  cent,  of  the  theoretical  value  as  the 
actual  h"  is  of  the  ideal  h". 

18.  For  the  Worthington  turbine  pump  of  Art.  53  and  for  which  curves 
are  shown  in  Fig.  58,  the  radius  of  the  point  " M"  (Fig.  46)  is  5.314  in.  and 
the  angle  a  =  28°.     For  1,700  r.p.m.  and  q  =  0.425  cu.  ft.  per  sec.,  compute 
the  value  of  h"  based  upon  the  velocity  diagram  at  M.     Compare  with- Fig. 
59.     (To  allow  for  leakage  assume  that  actual  discharge  through  the  im- 
peller =  1.100.) 

19.  For  the  De  Laval  pump  of  Art.  53  and  for  which  curves  are  shown  in 
Fig.  59,  the  radius  of  the  point  "M"  (Fig.  46)  is  3.81  in.  and  the  angle 
a  =  22°.     For  1,700  r.p.m.  and  q  =  1.3  cu.  ft.  per  sec.,  compute  the  value  of 
h"  based  upon  the  velocity  diagram  at  M.     Compare  with  Fig.  59.     (To 
allow  for  leakage  assume  that  the  actual  discharge  through  the  impeller 
=  1.03g.) 

20.  Compute  coefficients  A,  B,  and  C  as  in  problem  (13)  using  the  radius 
r2  for  shut-off  only  and  using  the  radius  of  "M"  for  reasonably  large  rates 
of  discharge.     Values  of  the  radii  of  M  will  be  found  in  problems    (18) 
and  (19). 


CHAPTER  VI 
CHARACTERISTICS 

62.  Definition  of  Characteristics. — The  curve  expressing 
the  relation  between  head  and  rate  of  discharge  of  a  centrifugal 
pump  running  at  a  constant  speed  has  been  called  the  "  character- 
istic" of  the  pump.  But  the  curves  of  brake  horse-power  and 
gross  efficiency  are  of  equal  commercial  importance  and  these 
three  together  as  in  Fig.  61  are  called  the  " characteristics" 
of  the  pump.  But  broadly  speaking  any  of  the  curves  expressing 


80 


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De  (Laval  Centrifugal  Pu|mp 
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s 

0.4      0.6      .0.8       1.0      1.2      1.4      1.6      1.8       2.0      2.2      .2.4      2.6 
Discharge-Cu.  .Ft.  per  Sec. 

FIG.  61. — Characteristics  of  a  6-inch  De  Laval  centrifugal  pump  at  a  con- 
stant speed. 

the  relations  between  the  head,  speed,  discharge,  and  horse- 
power may  be  termed  pump  characteristics  regardless  of  the 
variable  against  which  they  are  plotted.  From  a  set  of  curves 
such  as  in  Fig.  61,  however,  one  can  estimate  the  performance 
of  the  pump  under  any  conditions  of  operation. 

53.  Description  of  Pumps  Tested. — The  curves  shown  in  this 
chapter  are  from  actual  test  data  taken  by  the  author  upon  two 
centrifugal  pumps.  It  was  necessary  to  test  one  of  these  pumps 
at  one  speed  only  but  for  the  other  one  it  was  possible  to  vary 

88 


CHARACTERISTICS  89 

the  speed  from  700  to  2,000  r.p.m.  Sectional  views  of  these 
two  pumps  may  be  found  in  Figs.  62,  63,  64,  and  65.  The 
record  of  the  test  data  is  in  Appendix  A.  The  essential  di- 
mensions are  given  in  Tables  1  and  2. 

TABLE  1. — 2.5-iN.  TWO-STAGE  WORTHINGTON  TURBINE  PUMP 

Outer  radius  of  impeller  7*2  =  0 . 500  ft. 

Inner  radius  of  impeller  ri  =  0. 167  ft. 

Width  of  impeller  passage  B  =  0 . 250  in. 

Width  of  impeller  passage  BI  =  0.500  in. 

Vane  angle  at  exit  a2  =  26° 

Vane  angle  at  entrance  (approx.)  ai  =  15° 

Diffusion  vane  angle  (average)  A'z=  7.5° 

Area  of  impeller  passages  /2  =  0 . 0244  sq.  ft. 

Area  of  impeller  passages  (approx.)  /i  =  0.0260  sq.  ft. 

Area  of  diffuser  passages  F*  =  0.00895  sq.  ft. 

Number  of  diffusion  vanes  =  6 

Number  of  complete  impeller  vanes  =  5 

Number  of  partial  impeller  vanes  =  5 

Thickness  of  impeller  vanes  =  0.25  in. 

TABLE  2. — 6-iN.  SINGLE-STAGE  DE  LAVAL  VOLUTE  PUMP 

Outer  radius  of  impeller  r2  =  0 . 380  ft. 

Inner  radius  of  impeller  r\  =  0 . 182  ft. 

Width  of  impeller  passage  B  =  1 . 10  in. 

Width  of  impeller  passage  (total)  BI  =  1.75  in. 

Vane  angle  at  exit  a2  =  27° 

Vane  angle  at  entrance  (approx.)  di  =  10° 

Area  of  impeller  passages  /2  =  0.0706  sq.  ft. 

Area  of  impeller  passages  (approx.)  /i  =  0.0400  sq.  ft. 

Area  of  volute  F3  =  0 . 0652  sq.  ft. 

Number  of  impeller  vanes  =  6 

Thickness  of  impeller  vanes  =  0. 187  in. 

The  value  of  BI  is  the  sum  of  the  widths  for  both  sides  in 
the  case  of  the  double  suction  impeller.  The  value  of  F$  is 
the  area  of  the  volute  at  the  maximum  section  360°  from  the 
beginning.  Exact  values  of  ai  and  /i  are  difficult  to  estimate. 

54.  Head-discharge  Curves  at  Constant  Speed. — The  re- 
lation between  head  and  rate  of  discharge  for  eight  different 
speeds  is  shown  in  Fig.  66.  It  will  be  noted  that  this  particular 
pump  has  a  rising  characteristic  and  that  values  of  head  are 
obtained  which  are  greater  than  uz2/2g.  While  there  are  varia- 
tions due  to  slight  irregularities  in  the  test  data,  the  following 
values  will  be  fair  averages.  For  the  shut-off  head,  h  =  1.02 


90 


CENTRIFUGAL  PUMPS 


u22/2g;  for  the  maximum  head,  h  =  l.Q8u22/2g;  and  for  the  head 
at  the  point  of  highest  efficiency,  h  =  0.94^22/2#.  For  the 
curves  in  Fig.  61  the  corresponding  values  of  these  factors  are 
0.96,  0.985,  and  0.80  respectively. 

It  will  be  noticed  that  for  small  rates  of  discharge  the  curves 
in  Fig.  66  are  concave  upward  and,  after  passing  a  point  of 


FIG.  62. — Construction  of  6-inch   De  Laval   Centrifugal  pump. 

inflection,  they  assume  the  customary  form  of  concave  down- 
ward. The  reason  for  this  is  that  the  " churning  loss"  shown 
in  Fig.  58  prevents  the  head  from  rising  as  it  would  do  otherwise. 
But  this  factor  drops  out  as  the  rate  of  discharge  increases. 
This  feature  is  very  common  but  is  not  usually  noticed  by 
observers  because  an  insufficient  number  of  points  are  recorded 


CHARACTERISTICS 


91 


for  these  small  flows  to  enable  an  accurate  curve  to  be  drawn. 
Thus,  if  the  first  point  only  after  shut-off  had  been  omitted  from 


Discharge 


Suction 

FIG.  63. — Two-stage  Worthington  turbine  pump. 


Impeller  made  in  Halves  Riveted   H~  ^V7"7* ,~ 
together  with  15-^'Tobta  Bronze'mvete      ?> '-'  '' 


15-fc.TB.  Rivets 


FIG.  64. — Impeller  for  Worthington  turbine  pump. 

most  of  the  curves  in  Fig.  66,  there  would  be  no  indication  that 
the  true  curve  should  have  a  point  of  inflection.     The  same  is 


92 


CENTRIFUGAL  PUMPS 


true  in  Fig.  11  for  an  entirely  different  pump.  In  many  cases, 
such  as  Fig.  61,  the  curvature  for  this  portion  of  the  curve  is  so 
slight  that  no  point  of  inflection  could  be  detected. 

Another  noticeable  feature  of  the  curves  in  Fig.  66  is  that 
they  are  all  similar  in  shape  until  a  rate  of  discharge  of  about 
0.45  cu.  ft.  per  sec.  is  reached.  After  that  point  they  be- 
come very  steep,  and  the  higher  the  speed  the  steeper  they 
become.  According  to  the  theory  we  should  be  able  to  transfer 
readings  taken  at  any  speed  to  another  speed  and  obtain  the 
true  curve  at  the  latter  speed.  It  is  found  that  this  can  be 
done  for  values  of  discharge  less  than  0.45  cu.  ft.  per  sec.  but 


FIG.  65. — Diffuser  for  Worthington  turbine  pump. 

above  that  value  the  curves  at  different  speeds  will  not  agree 
with  each  other.  It  is  believed  that  a  series  of  curves  for  speeds 
below  900  r.p.m.  would  agree  with  each  other  if  they  were  re- 
duced to  some  one  common  speed.  It  is  thus  evident  that  the 
cause  of  the  disagreement  is  a  function  of  an  absolute  value 
of  the  rate  of  discharge  and  not  a  function  of  the  speed.  It  is 
believed  that  the  explanation  is  that,  at  about  the  rate  of  dis- 
charge mentioned,  the  absolute  pressure  at  entrance  to  the  im- 
peller becomes  so  low,  due  to  the  high  velocity  in  the  suction 
pipe  with  a  consequent  loss  of  head,  that  "cavitation"  is  set 
up  in  the  eye  of  the  impeller.  That  is,  the  eye  of  the  im- 


CHARACTERISTICS 


93 


o.i 


0.2  0.3  0.4 

Discharge-Cu.  Ft.  per  Sec. 

Worthington  Turbine  Pump 


FIG.  66. — Relation  between  head   and   discharge  at  various  speeds. 


01         0.2         0.3         0.4         0.5        0.6 
Discharge  in  Cu.Ft.  per  Sec. 

FIG.  67. — Pressures  in  case  between  first  and  second  stages. 


94 


CENTRIFUGAL  PUMPS 


peller,  and  consequently  the  impeller  passages,  is  not  completely 
filled  with  water.  Thus  the  actual  rate  of  discharge  of  the 
pump  is  decreased  below  the  expected  amount. 

This  cavitation  may  make  itself  apparent  even  where  the  pump 
is  tested  at  one  speed  only.  It  is  indicated  by  an  abrupt  break 
in  the  smoothness  of  the  curve  or  by  a  marked  increase  in  the 
steepness  of  the  curve  for  the  larger  discharges. 


o.i 


0.5 


0.6 


0.2  0.3  0.4 

Discharge  -  Cu.  Ft.  per  Sec. 

FIG.  68. — Relation  between  power  and  discharge  for  Worthington  turbine 

pump. 


Readings  were  also  taken  of  the  pressures  at  the  top  of  the 
first  stage,  where  the  pipe  (Fig.  63)  for  the  suction  gland  seal 
and  water  cooling  the  thrust  bearings  is  tapped  in.  These  pres- 
sures are  shown  in  Fig.  67  and  indicate  that  the  velocity  head  is 
very  high  at  this  point. 

55.  Power-discharge  Curves  at  Constant  Speed. — The  rela- 
tion between  brake  horse-power  and  the  rate  of  discharge  is 
shown  in  Fig.  68.  It  will  be  noticed  that  the  power  increases  as 
the  discharge  increases  for  the  smaller  speeds  but  for  the  higher 
speeds  the  power  attains  a  maximum  and  then  decreases.  The 


CHARACTERISTICS 


95 


explanation  for  this  is  involved  in  the  explanation  of  the  rapid 
drop  of  head  under  the  same  conditions. 

It  is  desirable  that  the  power  curve  should  drop  off  for  the 
maximum  rates  of  discharge  as  shown  in  Fig.  61.  .This  makes  it 
possible  to  install  a  motor  or  other  source  of  power  whose  maxi- 
mum capacity  is  but  little  more  than  the  power  required  under 
normal  operation.  This  is  conducive  to  low  cost  of  the  machine 
and  to  a  better  efficiency  of  the  motor.  If,  due  to  a  break  in 
the  pipe  line  or  some  other  cause,  the  head  becomes  very  low, 


0          0.1          0.2         0.3         0.4          0.5        0.6 
Discharge  -  Cu.Ft.  per  Sec. 

FIG.  69. — Water  horse-power  of  Worthington  turbine  pump. 

the  motor  will  not  then  be  overloaded.  This  feature  can  be 
attained  in  the  design  either  by  " throttling"  at  the  eye  of  the 
impeller  so  as  to  produce  cavitation  or  by  making  the  angle  az 
small. 

56.  Efficiency-discharge  Curves  at  Constant  Speed. — There 
are  no  peculiar  features  of  the  curves  in  Fig.  70  except  that  the 
maximum  efficiency  is  not  the  same  for  all  the  speeds.  The 
explanation  of  this  will  be  taken  up  later.  The  dash  curve  shown 
is  similar  to  the  single  efficiency  curves  and  is  an  envelop  of 
them.  It  shows  that  the  highest  efficiency  is  obtained  at  a  speed 
of  1700  r.p.m.,  when  the  discharge  is  about  0.4  cu.  ft.  per  sec. 


96 


CENTRIFUGAL  PUMPS 


57.  Impending  Delivery  or  Shut-off. — In  Fig.  71  will  be  found 
values  of  the  head  and  horse-power  for  impending  delivery  as 


0.2  0.3  0.4 

Discharge-Cu.  Ft.  per  Sec. 
Worthington  Turbine  Pump 


0.5 


0.6 


FIG.  70. — Efficiency  curves  at  various  speeds. 


0     200    400 

FIG.  71.  —  Values  of  head  and  power  for  impending  delivery. 


600    800    1000    1200   1400    1600    1800   2000 
R.  P.  M. 


well  as  the  power  consumed  in  bearing  and  gland  friction  for 
speeds  up  to  2,000  r.p.m.     It  will  be  found  that 


CHARACTERISTICS 


97 


h  =  0.00008657V2 

B.h.p.  =  0.00000000397V2-9 

=  O.OQ3U1-45 

58.  Maximum  Efficiency  —  Speed.  —  In  Fig.  72  will  be  found 
the  curve  showing  the  relation  between  efficiency  and  speed,  the 
efficiency  being  the  maximum  at  each  speed.  This  curve  shows 
that  the  highest  efficiency  will  be  found  at  about  1,700  r.p.m. 
but  that  very  good  results  could  be  obtained  with  quite  a  wide 
range  of  speeds. 


200          400 


600 


1800       20005 


800         1000        1200        1400 
K.  P.  M. 

FIG.  72.  —  Conditions  for  maximum  efficiency  of  Worthington  turbine  pump 

at  various  speeds. 

For  each  speed  the  maximum  efficiency  will  be  found  only  for 
a  certain  value  of  head  and  discharge  and  values  of  these  other 
quantities  are  also  plotted.  The  normal  discharge  is  seen  to 
follow  a  straight-line  law:  The  following  relations  will  be 
found  : 

q  =  0.0002357V 

h  =  0.0000827V2 

B.h.p.  =  0.00000001747V2- 


Since  q  varies  as  TV  and  h  .  jip.rip.a  R,S  TV2.,  t]hf  writer  hnrri" 
woulcTvary  afJV^T^JJut  the  efficiency  is  not  constant  for  all 
Speeds,  thereforethe  brake  horse-power  does  not  vary  as  the 
cube  of  the  speed.  In  the  present  case  the  efficiency  is  increasing 
for  the  most  part  as  the  speed  increases.  Therefore  the  brake 
horse-power  does  not  increase  as  rapidly  as  the  water  horse- 

7 


98 


CENTRIFUGAL  PUMPS 


power.  If  we  had  values  of  these  quantities  up  to  about 
3,000  r.p.m.  we  should  probably  find  another  law  for  the  brake 
horse-power  to  hold  above  1,700  r.p.m. 

59.  Zero  Lift  and  Maximum  Discharge. — When  the  head  is 
zero  the  rate  of  discharge  is  a  maximum  and  the  efficiency  is 
zero,  since  no  useful  work  is  done.  This  case  is  of  no  practical 
importance.  The  relation  between  maximum  discharge  and 
speed  may  be  seen  in  Fig.>7£  by  noting  that  it  is  the  same  as  the 
curve  for  zero  efficiency.  It  is  seen  to  be  a  straight  line  up  to 
about  a  speed  of  900  r.p.m.  and  a  discharge  of  about  0.4  cu.  ft. 
per  sec.'  This  offers  some  reason  for  the  statement  made  on 
page  92.  This  curve  would  appear  to  indicate  that  the  pump 


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300 
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0     200    400    600    800    1000   1200    1400 
R.  P.  M. 


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FIG.  73. — Constant  discharge  and  variable  speed. 


discharge  could  not  exceed  a  certain  value  no  matter  how  high 
the  speed.  Therefore  the  equation  offered  for  the  normal  rate  of 
discharge  in  Art.  58  would  not  be  true  for  too  large  a  value  of  N. 
60.  Constant  Discharge — Variable  Speed. — Fig.  73  shows  the 
performance  of  a  pump  delivering  a  constant  amount  of  water 
under  a  variable  head.  In  order  that  it  shall  do  that,  thg^see^d 
rjaust  be  varied.  Such  a  case  might  be  found  where  a  pump  is 
required  to  supply  a  fixed  amount  of  water  to  a  condenser  while 
the  level  of  the  source  of  supply  fluctuates  within  wide  limits. 
(Of  course  this  particular  pump  is  unsuited  for  condenser  pur- 


CHARACTERISTICS 


99 


poses  as  its  capacity  is  too  small  and  the  head  too  high,  but  the 
curves  will  illustrate  the  case  for  a  pump  that  is  suitable.)  It 
may  be  seen  from  the  curves  that  the  efficiency  varies  but  little 
over  quite  a  wide  range  of  head. 

In  the  particular  curves  shown,  the  efficiency  will  be  within 
5  per  cent,  of  the  maximum  possible  with  this  rate  of  discharge 
while  the  head  varies  from  22  ft.  to  205  ft.  The  particular  rate 
of  discharge  for  these  curves  is  0.20  cu.  ft.  per  sec.  Similar  curves 
would  be  obtained  for  other  discharges.  For  a  larger  discharge 
the  speed  for  zero  head  would  be  higher  and  the  first  part  of  the 


0.5 


0.4 


0.3 


0.2 


0.1 


30  £ 


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Xurbtne  Pum 


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12 


500  600    700    800    900   1000  1100  1200  1300  1400  1500  1600  1700  1800  1900  2000 
&FJC. 

FIG.  74. — Constant  head  and  varying  speed. 

efficiency  curve  would  not  be  so  steep,  also  the  peak  of  the  effi- 
ciency curve  would  be  shifted  over  to  a  higher  speed. 

61.  Constant  Lift — Variable  Speed. — The  case  of  a  constant 
head  and  a  variable  rate  of  discharge  is  shown  in  Fig.  74.  Such 
a  case  might  be  met  with  where  a  pump  lifted  water  vertically 
through  a  short  stretch  of  pipe  or  perhaps  discharged  directly 
into  a  stand-pipe  so  that  friction  losses  were  negligible  in  com- 
parison with  the  static  lift. 

For  quantities  of  water  varying  from  0.1  to  0.4  cu.  ft.  per  sec. 
for  a  head  of  50  ft.,  the  range  of  speed  is  seen  to  be  small.  Also 
the  efficiency  does  not  depart  widely  from  the  maximum  value 
possible  within  that  range.  But  for  rates  of  discharge  above 
0.4  cu.  ft.  per  sec.  the  efficiency  would  fall  rapidly. 


100 


CENTRIFUGAL  PUMPS 


It  will  be  noted  that  for  small  quantities  of  water  (in  the 
present  instance  anything  under  0.13  cu.  ft.  per  sec.),  the  speed 
necessary  will  be  less  than  that  required  to  maintain  the  static 
pressure  of  50  ft.  without  discharge.  This  is  due  to  the  character- 
istic being  a  rising  one. 

62.  Constant  Static  Lift  with  Friction — Variable  Speed. — A 
far  more  common  case  than  the  preceding  is  one  where  the  pump 
has  to  lift  water  a  fixed  vertical  height  and  where  the  pipe  line 
is  long  enough  to  add  a  substantial  friction  head.  In  fact  it  is 


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500  600-  700  800  900  1000  1100  1200  1300  1400  1500  1600  1700  1800  190D  2000 
R.P.M. 

FIG.  75. — Constant  static  lift  with  friction  head  and  varying  speed. 

possible  for  the  friction  head  to  be  greater  than  the  vertical  lift. 
Thus  both  the  head  and  the  rate  of  discharge  vary  together  since 
the  former  is  a  function  of  the  latter. 

It  will  be  noted  in  Fig.  75  that  the  efficiency  curve  is  very  steep 
at  the  beginning  and  very  flat  for  the  greater  portion  up  to  about 
1,800  r.p.m.  Thus  the  average  operating  efficiency  under  all 
conditions  shown  wilL  be  excellent.  If  the  static  lift  were  zero 
and  the  friction  head  were  properly  proportioned,  it  would  be 
possible  for  the  relation  between  h  and  q  to  follow  the  dotted  line 
in  Fig.  66  for  the  case  of  maximum  efficiency.  Thus  we  should 
obtain  the  maximum  efficiency  possible  under  all  conditions  of 
operation.1  For  the  particular  equation  chosen  for  these  curves, 

1  The  above  discussion  is  concerned  with  the  efficiency  of  the  pump  alone, 
not  with  the  combined  efficiency  of  the  pump  and  pipe  line.  For  the  latter 
see  Art.  64. 


CHARACTERISTICS.  101 

h  =  50  +  700#2,  the  relation  between  h  and  q  is  a  rough  approxi- 
mation to  this  dotted  curve  in  Fig.  66.  (See  Fig.  76.)  The  two 
are  identical  when  the  flow  is  about  0.26  cu.  ft.  per  sec.  For 
smaller  values  of  q  the  values  of  h  are  slightly  above  this  dotted 
curve  and  for  larger  values  than  0.26  the  values  of  h  are  below 
the  curve.  In  either  event  the  efficiency  of  the  pump  will  be 
less  than  the  maximum  of  which  it  is  capable.  But  for  any  given 
pipe  line  conditions  the  best  average  operating  efficiency  will  be 
obtained  when  the  speed  of  the  pump  is  varied  to  suit  the  head 
and  discharge. 

It  may  be  seen  that  the  case  taken  for  these  curves  is  inter- 
mediate between  the  cases  of  constant  discharge  and  constant 
lift.  With  different  static  lifts  and  with  different  friction  heads 
we  should  have  obtained  other  values  either  more  or  less  favorable 
than  those  shown  in  Fig.  75. 

It  might  be  thought  that  the  portion  of  the  curves  of  Fig.  74 
which  is  below  760  r.p.m.  would  be  a  field  of  instability  as  there 
are  two  values  of  the  discharge  for  one  value  of  speed.  Such 
might  be  the  case,  if  it  were  not  for  the  balancing  effect  of  fric- 
tion, however  slight  the  latter  might  be.  It  is  seen  in  Fig.  75, 
where  friction  is  introduced,  that  there  are  no  double  values. 
It  is  hardly  possible  to  have  a  condition  where  friction  is  en- 
tirely absent.  Thus  if  the  discharge  tends  to  increase  to  the 
larger  value  at  the  same  speed,  the  additional  head  required 
prevents  the  change.  Or  if  the  discharge  tends  to  decrease  to  a 
smaller  value,  the  resultant  diminution  of  the  friction  would 
lower  the  head  and  thus  prevent  the  discharge  from  assuming  the 
lower  value.  Any  real  instability  would  be  encountered  only 
where  the  lift  was  absolutely  constant  and  totally  independent 
of  the  discharge. 

63.  Constant  Static  Lift  with  Friction— Constant  Speed.— 
In  the  preceding  case  the  speed  of  the  pump  was  supposed  to  be 
varied  to  meet  the  demands  of  the  different  rates  of  discharge. 
In  the  present  case  the  pump  is  assumed  to  run  at  a  constant 
speed  of  1,800  r.p.m.,  while  the  conditions  of  the  lift  are  the  same 
as  before.  Since  the  head  developed  by  the  pump  may  be  much 
greater  than  the  head  required  to  produce  a  certain  flow  through 
the  pipe  line,  it  will  be  necessary  to  throttle  it.  Thus  a  great 
portion  of  the  work  done  by  the  pump  may  be  wasted.  There- 
fore the  actual  efficiency  of  the  pump  will  be  less  than  the 
efficiency  of  which  it  is  really  capable. 


102 


CENTRIFUGAL  PUMPS 


When  the  head  developed  by  the  pump  is  equal  to  the  head 
required  to  produce  that  same  flow  through  the  pipe  line,  no 
throttling  is  required.  It  is  evident  from  Fig.  76  that  this  point 
also  determines  the  maximum  rate  of  discharge  that  is  possible. 

The  curve  in  Fig.  76  designated  " pumping  efficiency"  is  the 
ratio  of  the  actual  water  horse-power  delivered  by  the  pump  to 
the  brake  horse-power.  As  may  be  seen  by  comparing  this  with 
Fig.  70,  throttling  has  caused  a  considerable  decrease  in  the  effi- 
ciency for  every  point  except  that  of  maximum  discharge,  where 


a 

0.1  "^       0.2  0.3  0.4  0.5 

Discharge  •  Cu.  Ft.  per  Sec. 

FIG.  76. — Constant  static  lift  with  friction  head  and  constant  pump  speed. 

throttling  is  absent.  Thus  a  pump  that  delivers  widely  varying 
quantities  of  water  must  have  a  low  overall  pumping  efficiency, 
if  it  is  compelled  to  run  at  a  constant  speed.1  By  comparing 
this  with  Fig.  75  it  may  be  seen  that  it  is  much  more  desirable 
to  vary  the  speed  of  the  pump  than  to  throttle  it  so  far  as  effi- 
ciency is  concerned. 

This  case  is  not  quite  so  bad  as  it  appears  when  we  consider 
also  the  efficiency  of  the  motor  or  prime  mover.  Usually  the 

1  The  difference  between  the  pump  efficiency  and  the  overall  pumping 
efficiency  is  that  the  head  developed  by  the  pump  is  used  in  computing  the 
former,  while  the  actual  lift  of  the  pump  including  pipe  friction  but  not 
the  throttling  loss  is  used  for  the  latter. 


CHARACTERISTICS  103 

efficiency  of  the  latter  will  be  somewhat  better  when  it  is  run 
at  a  constant  speed.  When  we  consider  the  additional  losses  in- 
volved in  operating  the  motor  or  prime  mover  at  a  varying  speed, 
we  find  that  the  difference  in  the  economy  of  the  set  under  these 
two  conditions  of  operation  is  not  so  great  as  for  the  pump  alone. 

Whether  efficiency  is  a  determining  factor  or  not  is  open  to 
question.  In  general  the  use  of  a  variable  speed  drive  will  require 
a  greater  investment  as  it  is  not  as  cheap  as  a  constant-speed 
drive.  Also  the  variable  speed  device  requires  more  intelligence 
in  its  operation  and  will  be  more  trouble  to  tend  and  keep  in 
repair.  Thus  the  cost  of  labor  will  be  higher.  It  may  be  de- 
sirable to  sacrifice  efficiency  for  cheapness  in  first  cost  and 
simplicitv^of  operation. 

64.  Efficiency  of  Pump  and  Pipe  Line. — The  preceding 
discussion  has  been  concerned  with  the  efficiency  of  the  pump 
alone.  If  the  pipe  line  is  considered  along  with  the  pump  our 
results  will  be  somewhat  altered.  The  efficiency  of  a  pipe  Jine 
may  be  defined  as  static  lift  -s-  (static  lift  +  friction  head) . 
In  order  that  the  efficiency  of  a  pipe  line  shall  be  the  maximum 
possible,  which  is  100  per  cent.,  it  is  necessary  for  the  flow  to  be 
zero  in  order  that  the  friction  head  may  be  zero.  Practically 
if  the  pipe  is  very  short  in  proportion  to  the  vertical  height  to 
which  water  is  raised,  such  as  is  the  case  where  water  is  de- 
livered into  a  stand-pipe  close  to  the  pump,  this  condition  would 
be  approached  very  closely  even  with  a  flow  of  considerable 
magnitude.  The  per  cent,  of  friction  head  allowable  depends 
upon  the  lift  and  the  length  of  the  pipe.  If  thejnpe  is  very  long 
amijhejij^  woulp1  be  too  costlv  to  make^the  pipe  Jine 

efficiency  high  for  the  normal  rate  of  flow.  The  most  economical 
size  of  pipe  would  be  such  that  the  interest  on  the  cost  of  the  pipe 
would  equal  the  annual  cost  of  the  power  wasted  in  pipe  fric- 
tion. Under  these  conditions  the  total  cost,  which  is  the  sum 
of  these  two,  is  a  minimum. 

For  the  case  where  the  efficiency  approaches  100  per  cent, 
the  combined  efficiency  of  the  pump  and  the  pipe  line  would 
approach  the  efficiency  curve  shown  in  Fig.  74,  since  this  is 
where  the  friction  head  is  zero.  For  the  case  where  loss  of 
head  is  considerable,  such  as  in  Fig.  75,  the  combined  efficiency 
of  the  pump  and  pipe  line  would  be  far  below  the  efficiency  curve 
for  the  pump  alone  that  is  there  shown.  In  fact  it  would  be 
below  the  efficiency  curve  in  Fig.  74.  Likewise  the  curve  for 


104 


CENTRIFUGAL  PUMPS 


pumping  efficiency  in  Fig.  76  is  higher  than  the  curve  would  be 
if  the  static  lift  only  were  considered  as  useful  work. 

65.  Characteristic  Curves. — All  of  the  relations  shown  in 
the  preceding  sets  of  curves  are  involved  indirectly  at  least 
in  what  may  be  called  the  characteristic  curves,  two  forms  of 


o.i 


0.2  0.3  0.4 

Discharge-Cu.  Ft.  per  Sec. 

.Iso-Efficiency  Curves-Worth! ngton  Pump 

FIG.  77.— Characteristic  diagram. 


0.5 


0.6 


which  are  shown  in  Figs.  77  and  78.  In  Fig.  77  we  have  the 
usual  head-discharge  curves  at  various  constant  speeds  and  upon 
these  are  superimposed  iso-efficiency  curves.1  In  Fig.  78  we  have 

1  To  plot  these  curves  it  is  possible  to  write  the  value  of  the  efficiency 
alongside  of  each  experimental  point  for  which  the  head-discharge  curves 
are  drawn.  Then  the  iso-efficiency  curves  may  be  drawn  by  interpolation. 


CHARACTERISTICS 


105 


something  that  is  analogous  to  the  characteristic  curve  for  a 
hydraulic  turbine  as  the  coordinates  are  speed  and  discharge. 
(However,  these  coordinates  represent  actual  values  and  not 
values  under  a  unit  head.)  Upon  this  diagram,  we  draw  iso- 
head,  iso-power,  and  iso-efficiency  curves. 

By  the  use  of  these  diagrams  it  is. possible  to  tell  at  a  glance 
what  the  conditions  of  operation  might  be  under  any  circum- 
stances and  it  is  easily  seen  what  is  the  most  economical  field 
of  operation.  It  is  clear  that,  though  the  maximum  efficiency 
will  be  found  for  one  point  only,  a  centrifugal  pump  may  be 


200         400 


1800        2000 


E.P.M. 

FIG.  78. — Characteristic  diagram. 


used  under  quite  a  range  of  values  of  head,  speed,  and  discharge 
without  suffering  a  big  drop  in  efficiency.  Thus  for  this  particu- 
lar pump  the  field  in  which  the  efficiency  is  above  50  per  cent. 
or  within  5.5  per  cent,  of  the  maximum  is  quite  large. 


66.  PROBLEMS 

1.  Assuming  that  <f>  for  shut-off  in  Fig.  11  is  1.0,  compute  the  factors  by 
which  u«2/2g  must  be  multiplied  to  give  the  maximum  head  with  the  rising 
characteristic  and  values  of  head  for  the  maximum  efficiency  with  all  three 
of  the  curves. 

The  writer  believes  it  is  easier,  however,  to  construct  the  efficiency  curves 
as  in  Fig.  70.  For  any  value  of  the  efficiency  for  which  a  curve  is  desired  in 
Fig.  77  it  is  possible  to  read  values  of  q  for  the  various  speeds  from  Fig.  70. 
Thus  the  points  are  located  where  each  iso-efficiency  curve  intersects  each 
head-discharge  curve  in  Fig.  77. 


106  CENTRIFUGAL  PUMPS 

2.  What  are  values  of  </>  for  the  above? 
Ans.  0.865,  0.900,  1.08,  1.25  respectively. 

3.  What  is  the  efficiency  of  the  pipe  line  in  Fig.  76  when  q  =  0.4  cu.  ft. 
per  sec.? 

Ans.  0.312. 

4.  What  is  the  combined  efficiency  of  the  pump  and  pipe  line  in  Fig.  76 
when  q  =  0.4  cu.  ft.  per  sec.? 

Ans.  0.103. 

5.  What  would  be  the  combined  efficiency  of  the  pump  and  pipe  line  in 
Fig.  75  when  q  =  0.4  cu.  ft.  per  sec.? 

Ans.  0.166. 

6.  For  a  case  of  variable  speed  plot  the  curve  for  the  efficiency  of  the  pump 
and  pipe  line  using  the  same  law  for  the  total  lift  as  given. 

7.  A  flow  of  2.0  cu.  ft.  of  water  per  sec.  is  to  be  raised  100  ft.     If  the  di- 
ameter of  the  pipe  is  6  in.  and  its  length  is  120  ft.,  find  the  pipe  line  efficiency. 
(Assume  m  =  0.03  and  neglect  all  minor  losses.) 

Ans.  0.896. 

8.  If  the  length  of  the  pipe  in  (7)  were  1,200  ft.,  what  would   be  the 
efficiency  if  all  other  quantities  are  the  same? 

Ans.  0.462. 

9.  If  the  diameter  of  the  pipe  is  8  in.  and  the  length  1,200  ft.,  what  would 
be  the  efficiency  of  the  pipe  line,  all  other  conditions  being  the  same  as  in  (7)  ? 

Ans.  0.780. 


CHAPTER  VII 
DISK  FRICTION 

67.  Definition. — An  important  source  of  loss  of  power  in  cen- 
trifugal pumps  is  the  drag  of  the  impeller  through  the  water  in 
the  clearance  spaces.     This  is  termed  disk  friction. 

The  results  given  in  this  chapter  were  determined  by  experi- 
ments made  by  Gibson  and  Ryan,1  and  are  the  most  accurate 
and  comprehensive  tests  of  which  the  author  is  aware.  The 
disks  were  of  9-in.  and  12-in.  diameter  and  with  various  kinds  of 
surfaces,  the  speeds  were  varied  from  450  to  2,200  r.p.m.,  and  the 
side  clearance  from  %  in.  to  2-J£  in. 

68.  Theory. — The  frictional  resistance  per  sq.  ft.  of  the  disk 
may  be  taken  as  equal  to  fun,  where  u  is  the  velocity  of  the 
area    in  feet   per  sec.    and  /  and  n  are   experimental   factors. 
The  resistance  offered  by  an  elementary  annular  ring  will  then 
be  equal  to  /  X  lirrdr  X  un.     Since  u  =  rco,  the  moment  of  the 
resistance  may  be  expressed  as 

2irfunrn+2dr 

The  moment  of  the  resistance  of  the  two  faces  of  the  disk  of  radius 
R(H.)  will  be 

CR 

T'  =  47r/con  I     rn+2dr 

Jo 


Tr  =  R«+*  (ft.  lb.)  (57) 

n  ~T-  o 

If  the  edge  of  the  disk  has  an  appreciable  thickness  b  (ft.)  the 
moment  of  the  resistance  of  the  edge  will  be  2'MunRn+?J  Adding 
this  to  the  value  in  (57),  the  total  torque  exerted  by  the  water 
upon  the  disk  is 

T  =  2Trfu«R"+*  (^~^  +  b)  (ft.  lb.)  (58) 

From  the  above  it  may  be  seen  that,  if  b  is  small  compared 
with  R,  the  effective  radius  is  approximately 

R'  =  (1  +  b/2R)R  (59) 

1  "Resistance  to  Rotation  of  Disks  in  Water  at  High  Speeds/'  Proc.  of 
the  Inst.  of  Civ.  Eng.,  1910,  Vol.  179,  p.  313. 

107 


108 


CENTRIFUGAL  PUMPS 


By  effective  radius  is  meant  the  radius  of  a  disk  the  friction  on 
whose  faces  alone  is  equal  to  the  total  resistance  of  the  faces  and 
edge  of  the  actual  disk.  The  power  consumed  in  disk  friction 
will  then  be 


H  p  = 


(60) 


550(n  +  3) 

Equation  (60)  applies  to  a  solid  disk.  If  it  is  desired  to  con- 
sider an  annular  ring  it  is  necessary  to  integrate  between  the 
limits  of  RI  and  J?2  rather  than  0  and  R.  In  equation  (59)  we 
should  use  R2  for  computing  R' .  With  Rf  thus  obtained  we  should 
have 


H.p.  * 


(61) 


550(n  +  3) 

69.  Experimental  Results. — Numerous  experiments  were  made 
by  Gibson  and  Ryan  to  determine  values  of  /  and  n  and  to  estab- 
lish the  laws  by  which  they  vary.  The  equations  in  Art.  68 
were  obtained  by  integration,  treating  /  and  n  as  constants. 
Experiment  seems  to  show  that  they  vary  as  the  velocity  and 
hence  are  functions  of  r  and  o>.  Since  they  are  functions  of 
r  the  integration  is  incorrect  and  the  equations  do  not  express 
the  exact  way  in  which  the  disk  friction  varies.  But  they  may 
be  used  as  empirical  equations  and  will  yield  correct  results 
providing  proper  values  of  /  and  n  are  selected. 

TABLE  3 


Disk 


Condition  of  case 

Mean  vel. 
ft.  per  sec. 

Polished  brass 

Rough  cast  iron 

/ 

n 

/ 

71 

10 

0.0031 

1.85 

0  .  0023 

2.00 

20 

0.0033 

1.84 

0.0027 

1.96 

Smooth,  painted  

30 

0  .  0035 

.83 

0.0032 

1.91 

40 

0.0037 

.82 

0.0037 

1.86 

50 

0.0039 

.80 

0.0042 

1.81 

10 

0.0029 

.92 

0.0025 

2.00 

20 

0.0033 

.89 

O.OQ27 

1.98 

Rough  cast  iron  

30 

0.0037 

1.86 

0.0028 

1.96 

40 

0.0041 

1.83 

0.0029 

1.93 

50 

0.0044 

1.80 

0.0030 

1.91 

For  the  usual  clearances  encountered  with  centrifugal  pumps 
the  average  values  in  Table  3  may  be   used.     Mean   velocity 


DISK  FRICTION  109 

was  taken  by  the  experimenters  as  being  the  velocity  of  a  point 
midway  between  the  inner  and  outer  radii  of  an  annular  ring  or 
one-half  the  peripheral  velocity  in  the  case  of  a  solid  disk.  This 
is  not  logical,  but  it  is  convenient,  and,  as  long  as  the  equations 
are  really  empirical  and  a  strict  mathematical  integration  appar- 
ently impossible,  it  is  as  good  as  any  other  procedure. 

70.  Summary  of  Results.  —  The  resistance  decreases  as  the 
temperature  of  the  water  increases.     The  effect  of  temperature  is 
negligible  when  n  =  2.0    and  becomes    more    important  as  n 
becomes  smaller. 

The  value  of  ^is_indepfiiident  of  the  clearance  but  the  value  of 
/.increases  as_tlie^cleararice  increases.  For  the  smooth  disk  in 
a  smooth  case  the  value  of  /  increased  about  10  per  cent,  as  the 
clearance  varied  from  JfJ  in.  to  2-J^  in.  There  was  very  little 
difference  within  this  range  of  clearance  for  the  rough  disk  in  a 
rough  case.  For  extremely  small  clearances  the  friction  is  some- 
what higher  than  the  minimum  possible.  As  the  clearance  is 
increased  the  friction  decreases  slightly.  The  minimum  value 
is  soon  reached,  however,  and  after  this  the  friction  increases 
with  the  amount  of  clearance. 

Both  /  and  n  vary  according  to  the  nature  of  the  surfaces  and 
the  speed.  The  friction  increases  as  the  surfaces  become  rougher. 
The  friction  of  a  smooth  disk  in  a  rough  case  is  about  the  same  as 
that  of  a  rough  disk  in  a  smooth  case. 

The  addition  of  ribs  to  one  of  the  disks  gave  an  increase  in 
the  power  consumed,  the  loss  being  greater  as  the  ribs  were  made 
deeper.  This  proves  the  shrouded  type  of  impeller  to  be  better 
thajn_the_arjen  type. 

71.  Approximate  Formulas.  —  Equations   (60)  and   (61)  are  a 
little  tedious  to  use  and  for  many  purposes  it  may  be  sufficient 
to  use  approximate   formulas.     Inserting  the  diameter  of  the 
impeller  D  in  inches  and  taking  n  =  2.00  we  have 


1,515,000,000,000 

Since  we  have  used  a  value  of  n  that  is  larger  than  the  average  we 
shall  offset  this  roughly  by  selecting  a  value  of  /that  is  too  small. 
With  /  =  0.002  we  have 

__  N*D*  (     } 

H*P-  ~  760,000,000,000,000 


110  CENTRIFUGAL  PUMPS 

Since  u2  =  0  \/2gh  and  also  u2  =  irD  AT/720,  we  may  insert  values 
of  /i  in  (63)  and  obtain 


72.  Conclusions.  —  It  is  desirable  to  use  a  shrouded  impeller 
rather  than  an  open  type.  The  impeller  should  be  polished  or 
made  as  smooth  as  is  feasible.  The  interior  of  the  case  should 
also  be  painted  so  as  to  give  it  a  smooth  surface.  All  clearances,) 
either  side  or  radial,  should  be  small. 

Either  equation  (64)  or  (65)  shows  that  for  a  given  head  it  is 
desirable  to  use  a  small  diameter  of  impeller  at  a  high  rotative 
speed  in  order  to  minimize  the  disk  friction. 

An  impeller  with  a  steep  characteristic  must  have  a  higher  value 
of  0  for  a  given  head.  For  such  a  case  the  disk  friction  must  be 
greater  than  that  of  a  corresponding  pump  with  a  flat  or  a  rising 
characteristic. 

73.  PROBLEMS 

1.  In  the  experiments  a  12-in.  polished  brass  disk  in  a  rough  cast-iron  case 
absorbed  1.11  h.p.  at  1,500  r.p.m.     See  how  close  you  come  to  this  quantity 
by  using  values  from  Table  3  and  the  various  formulas  that  may  be  applied. 
(b  =  0.0167  ft.) 

2.  What  will  be  the  power  consumed  by  a  6-in.  polished  brass  disk  in  a 
rough  cast-iron  case  when  running  at  3,000  r.prm.?     (6  same  as  in  (1)). 

3.  Assuming  <f>  =  1  J3,  what  is  the  disk  friction  of  a  12-in.  impeller  develop- 
ing a  head  of  150  ft.? 

4.  Assuming  <f>  =  1.0,  what  is  the  disk  friction  of  an  impeller  developing 
a  head  of  160  ft.  when  running  at  2,000  r.p.m. 

*  The  powers  of  h  may  be  found  very  conveniently  on  the  slide  rule  by 
noting  that  h1'6  =  h^/h  and  /i2-5  =  h2\/h. 


CHAPTER  VIII 
FACTORS  AFFECTING  EFFICIENCY 

74.  Efficiency  of  a  Single  Pump. — The  maximum  efficiency 
of  a  certain  pump  was  found  to  be  different  at  difeent  speeds 
as  may  be  seen  ir^Fig.  72.  It  is  now  proposed  to  show  why  the 
efficiency  of  a  pump  is  not  independent  of  the  speed.  It  will 
probably  be  true  that  the  hydraulic  efficiency  will  be  a  constant 
quantity  or  at  most  vary  but  little.  This  will  be  the  case,  since, 
as  is  pointed  out  in  Art.  39,  thfr Josses  of  head  a,reMi proportion^.] 
to  the  squares  of  the  velocities. (fffiut  the  sjguares  ojjbfa^  vpln^jgg 
concerned  are  in  direct  proportimi  to  the  head  developed.  Thus 
both  the  hydraulicjgssee-and"  the  w  a (iei'-^Qwer  output  of  thej^nmp 
follow  the  same  law,  thatjs  they  vary  as  the_three  halveslj)Qw.er 
of  jjie  Beacl  dey^lop&dLCt'he  rate  of  discharge  varie^As  the  square 
root  of  the  head),  or  as  the  cube  of  the  pump  speed/p  We  might 
conclude  the  same  thing  from  equation  (50)  which  fs  independent 
of  any  fixed  values  of  head  or  speed.  If  the  mechanical  losses 
followed  the  same  law  as  the  hydraulic  losses,  then  the  gross 
efficiency  would  also  remain  constant,  since  the  input  and  outrjut 
of  the  pump  would  vary  in  the  same  ratio. 

But  the  mechanical  losses  do  not  vary-as  the  cube  of  the  speed. 
For  the  Worthington  turbine  pump  for  which  Fig.  71  was  con- 
structed, the  power  lost  in  bearing  and  gland  friction  will  be 
approximately  represented  by  ,  ; 

H.p.  =  0.00003S4N1-39 

Since  the  bearing  and  gland  friction  does  not  increase  as  rapidly 
as  the  water  horse-power  with  an  increase  in  speed,  it  will  be- 
come of  less  percentage  value.  By  the  approximate  formula 
for  disk  friction,  equation  (63),  it  might  be  thought  that  the 
disk  friction  varied  at  the  same  rate  as  the  hydraulic  quantities, 
but  the  more  accurate  formula,  equation  (61),  together  with 
the  values  of  /  and  n  in  Table  3,  will  show  that  the  disk  friction 
increases  at  a  lower  rate  than  the  cube  of  the  speed.  Thus 
the  total  mechanical  losses  will  become  of  less  percentage  value 

111 


112 


CENTRIFUGAL  PUMPS 


as  the  speed  increases.  In  order  to  illustrate  this  point,  Table 
4  is  presented.  The  pump  to  which  these  values  apply  is  the 
Worthington  turbine  pump  of  Chapter  VI.  (See  Fig.  72.) 


TABLE  4 


Speed 

700  r.p.m. 

1,700  r.p.m. 

Bearing  friction  
Disk  friction  
Hyd.  lossep  and  leakage  
Water  horse-power 

0.35    h.p. 
0.27    h.p. 
0.29    h.p. 
0  75    h.p. 

1.20    h.p. 
3.00    h.p. 
4.40    h.p. 
10.70    h.p. 

Brake  horse-power 

1.66    h.p. 

19.30    h.p. 

Hyd.  and  vol.  efficiency  
Mechanical  efficiency  
Gross  efficiency  '.  

0.708 
0.627 
0.443 

0.708 
0.783 
0.555 

From  this  it  might  be  inferred  that  the  higher  the  speed, 
the  higher  the  efficiency,  and  that  the  gross  efficiency  would 
approach  the  hydraulic  efficiency  as  a  limit.  But  experiment 
shows  that  the  efficiency  does  not  increase  for  speeds  above 
1,700  r.p.m.  in  the  case  of  this  particular  pump,  but  falls  off 
slightly  instead.  The  explanation  of  this  drop  of  efficiency  is 
that  cavitation  or  some  other  phenomenon  affects  the  opera- 
tion of  the  pump.  It  may  be  seen  in  Fig.  66  that  the  point  of 
maximum  efficiency  at  1,700  r.p.m.  is  at  a  discharge  of  0.4  cu. 
ft.  per  sec.  and  the  latter  value  of  discharge  is  the  one  for  which 
certain  departures  from  assumed  laws  begin.  It  is  certain  that 
for  any  given  pump  the  efficiency  will  begin  to  decline  if  the 
speed  be  carried  high  enough. 

The  general  conclusion  is  that  for  any  single  pump  the  maxi- 
mum efficiency  of  which  it  is  capable  will  increase  at  a  fairly 
rapid  rate  as  the  speed  is  increased  above  a  very  small  value. 
For  higher  speeds  the  efficiency  will  change  more  slowly  as 
the  effect  of  the  mechanical  losses  becomes  of  less  percentage 
value.  As  the  speed  is  still  further  increased  the  efficiency  will 
attain  a  maximum  value  and  then  decrease,  due  to  the  introduc- 
tion of  some  new  source  of  loss. 

75.  Efficiency  of  a  Series  of  Pumps. — The  preceding  dis- 
cussion has  been  concerned  with  a  single  pump  operated  under 
various  conditions.  The  remainder  of  this  chapter  will  be  de- 
voted to  a  consideration  of  a  series  of  pumps  all  alike  in  every 


FACTORS  AFFECTING  EFFICIENCY 


113 


respect  except  for  the  one  variable  element  whose  effect  upon  the 
efficiency  will  be  studied.  By  efficiency  is  meant  the  maximum 
efficiency  of  which  any  pump  in  the  series  is  capable. 

76.  Type  of  Impeller. — By  the  term  "type  of  impeller"  is 
here  meant  the  ratio  of  the  diameter  of  the  impeller  to  its  width, 
that  is  D/B.  (See  Figs.  17  and  18.)  An  impeller  for  which 
this  factor  is  large  may  be  seen  in  Fig.  79,  while  one  with  a 
comparatively  low  value  of  the  ratio  is  shown  in  Fig.  21. 


FIG.  79. — Centrifugal  pump  with  narrow  type  of  impeller. 
(Goulds  Mfg.  Co.} 

Since  the  head  developed  by  an  impeller  is  a  function  of 
the  peripheral  speed,  it  follows  that  it  is  possible  to  obtain  a 
given  head  by  a  series  of  impellers  of  different  diameters  but 
running  at  different  rotative  speeds.  In  order  that  the  dis- 
charge shall  be  the  same  it  will  be  necessary  to  vary  the  width 
B  in  inverse  proportion  to  the  diameter  D,  so  as  to  keep  the 
discharge  area  the  same.  Thus  we  may  attain  a  given  head 
and  discharge  with  a  series  of  impellers  of  different  "  types.7' 

In  the  preceding  chapter  it  is  shown  that  for  a  given  periph- 
eral speed  the  disk  friction  will  be  less  in  the  case  of  a  small 


114 


CENTRIFUGAL  PUMPS 


diameter  of  impeller  at  a  high  rotative  speed  than  for  a  large 
diameter  of  impeller  at  a  low  rotative  speed.  Therefore, 
so  far  as  disk  friction  is  concerned,  we  should  expect  the  effi- 
ciency to  be  higher  the  smaller  the  value  of  the  ratio  D/B. 
That  this  is  so  may  be  seen  in  Fig.  80.  This  curve  was  drawn 
for  a  number  of  pumps  of  all  sizes-and  styles  so  that  scarcely  no 
two  pumps  differ  only  in  this  one  respect.  Since  the  efficiency 
is  also  affected  by  other  factors  so  that  the  effect  of  "type"  is 
sometimes  offset  by  other  considerations,  the  points  plotted 
will  not  all  lie  on  a  single  curve. 

If  it  is  necessary  to  develop  a  high  head  per  stage  at  a  low 
rotative    speed,  it  will    be    impossible    to  secure   a  low  value 


M 

° 

"> 

^ 

t 

o 

^ 

• 

.            0 

bU 

^5 

^*-< 

0 

W) 

"^8- 

•^. 

—  — 

—  —  -ll_^ 

40 

00 

0 

i 

i 

0 

2 

g 

j 

0 

4 

0 

0 

0 

t 

0 

7( 

Turbine  Pumps      Type=D/B 

FIG.'  80. — Efficiency  as  a  function  of  impeller  type. 

of  the  "type,"  unless  the  rate  of  discharge  should  also  be  very 
large.  But  even  in  that  event,  the  type  will  not  be  as  small 
as  it  would  if  a  higher  rotative  speed  could  be  employed. 

77.  Efficiency — Capacity. — The  efficiency  of  a  centrifugal  pump 
is  a  function  of  the  capacity,  head,  and  speed  but  the  most 
important  in  its  effects  is  the  capacity.1  This  is  so  much  so  that 
the  efficiency  is  sometimes  given  as  a  function  of  the  capacity 
to  the  exclusion  of  other  quantities. 

Suppose  that  a  series  of  impellers  of  the  same  diameter  are  of 
similar  design  so  that  they  develop  the  same  head  when  running 
at  the  same  speed,  but  that  their  widths  are  different  so  that 
their  capacities  are  different.  The  mechanical  losses  increase 
slightly  as  the  capacity  increases  due  to  the  larger  shaft  diam- 
eter and  weight  necessary  while  the  disk  friction  and  the  leakage 
losses  will  be  approximately  the  same  for  all  of  them.  The  hy- 

1  The  three  factors  together  really  involve  the  "type." 


FACTORS  AFFECTING  EFFICIENCY 


115 


sdll_xaj^L.at. about  the  same  rate  as 
therefore  the  hydraulic  effi- 
ciency may  be  said  to  remain  constant.  Actually  the  hydraulic 
efficiency  will  increase  slightly  as  the  capacity  increases,  since  it 
is  well  known  that  the  friction  of  water  flowing  through  large 


20 
0  100  200  300  400  500  600  700  800  900  1000  1100  1200  1300  1400  1300  1600  1700  1800 

Turbine  Purups,  Discharge  in  Gal.  per  Min. 

FIG.  81.  —  Efficiency  as  a  function  of  capacity. 

passages  is  less  than  through  smaller  passages.  Thus  as  the 
capacity  increases  the  hydraulic  efficiency  increases  s^ght.]yj  the 
mechanical  and  the  volumetric  etnclenc 


.fcW  an  illustration  let  us  consider  the  Worthington  pump 
for  which  the  curves  in  Chapter  VI  were  constructed.     At  1,700 


90 


0     100    200    300   400    500   600    700    800    900  1000  1100  1200  1300.1400  1500  1600  1700  1800 
Volute  Pumps,  Discharge  in  Gal.per  Min. 

FIG.  82. — Efficiency  as  a  function  of  capacity. 

r.p.m.  that  pump  delivered  0.4  cu.  ft.  of  water  per  sec.  at  a 
head  of  237  ft.  Let  us  estimate  the  efficiency  of  another  pump 
of  similar  design  but  capable  of  delivering  ten  times  as  much 
water  at  the  same  speed  and  head.  This  means  that  the  width 
of  the  second  impeller  must  be  2.5  in.  instead  of  the  0.25  in. 
as  in  the  present  pump.  The  comparison  is  shown  in  Table  5. 


116 


CENTRIFUGAL  PUMPS 
TABLE  5 


Discharge,  cu.  ft.  per  sec. 

0.40 

4.00 

\ 

Bearing  friction       

1.20h.p. 

4.  20  h.p. 

Disk  friction                

3.  00  h.p. 

3.  00  h.p. 

Leakage  loss     

2.00h.p. 

2.  00  h.p. 

Hydraulic  losses  

2.40  h.p. 

23.  00  h.p. 

Total  losses         

8.60h.p. 

'    32.  20  h.p. 

Water  horse-power  

10.  70  h.p. 

107.  00  h.p. 

Brake  horse-power                 

19.  30  h.p. 

139.  20  h.p 

Hydraulic  efficiency  

0.817 

0.823 

Volumetric  efficiency  
IVIechanical  efficiency 

0.867 

0.782 

0.985 
0.948 

Gross  efficiency                       

0.555 

0.769 

0         1,000       2,000       3,000       4,000       5,000       6,000       7,000       8,000       9,000      10,000 
Turbine  Pumps,  Discharge  in  Gal. "per  Min. 

FIG.  83. — Efficiency  as  a  function  of  capacity. 


2,000       4,000       6,000       8,000      10,000      12,000      14,000      16,000     18,000     20,000 
Volute  Pumps,  Discharge  in  Gal.  per  Min. 

FIG.  84. — Efficiency  as  a  function  of  capacity. 

For  a  number  of  pumps  of  all  varieties  average  efficiency 
curves  against  capacity  are  shown  in  Figs.  81,  82,  83,  and  84. 
Two  scales  have  been  used  in  order  that  values  of  efficiency  for  the 
usual  moderate  discharges  may  be  readily  obtained,  and  on  the 
other  hand  to  show  the  entire  field  covered.  As  there  is  some 


FACTORS  AFFECTING  EFFICIENCY 


117 


dispute  concerning  the  relative  merits  of  turbine  and  volute 
pumps,  the  efficiency  curves  for  the  two  have  been  plotted  sepa- 
rately. The  points  plotted  would  seem  to  indicate  that  the  tur- 
bine pumps  are  more  generally  used  for  the  smaller  discharges 
and  the  volute  pumps  for  the  larger.  It  may  also  be  seen  that 
the  volute  pumps  run  up  into  much  larger  capacities  than  the 
turbine  pumps. 

A  few  values  that  are  off  the  scales  of  these  curves  are:  For  a 
turbine  pump  of  28,530  G.P.M.  capacity  the  efficiency  was  81 
per  cent.  For  volute  pumps  of  24,000,  26,900,  125,500,  and 
132,000  G.P.M.  capacities  the  efficiencies  were  66.0,  72.0,  65.0, 
and  77.5  per  cent,  respectively. 

78.  Efficiency — Head. — For  the  single  pump  in  Art.  74  the 
efficiency  decreased  as  the  speed,  and  consequently  the  head, 


Efficiency-Percent 

§  ggg  8382 

3r- 

1 

a 

-U 

= 

Turbine  Pumps-Head  per  Stage  in  Feet 


0  100  200 

Volute  Pumps-Head  per  Stage  in  Feet 

FIG.  85. 

decreased.  But  the  rate  of  discharge  decreased  also.  We-  wish 
now  to  determine  the  effect  of  the  head  upon  a  series  of  pumps 
where  the  rate  of  discharge  is  the  same  for  all  of  them.  We 
shall  assume  that  the  impellers  are  to  be  of  the  same  diameter, 
therefore  it  will  be  necessary  for  the  rotative  speeds  and  the  im- 
peller widths  to  be  different. 

Let  us  illustrate  the  case  by  considering  the  Worthington  pump 
with  12-in.  impellers  running  at  1,700  r.p.m.  and  delivering 
0.4  cu.  ft.  of  water  per  sec.  against  a  head  of  237  ft.  Let  us 
assume  that  a  pump  of  similar  design,  but  with  a  wider  impeller, 
is  to  deliver  the  same  quantity  of  water  against  a  head  of  118.5 


118 


CENTRIFUGAL  PUMPS 


ft.  From  the  curves  in  Fig.  72  the  speed  will  be  found  to  be  1,200 
r.p.m.  Since  the  impeller  passages  are  somewhat  wider,  the 
hydraulic  losses  ought  to  be  of  a  slightly  smaller  percentage  value 
but  we  shall  assume  that  they  are  the  same.  The  two  cases 
may  be  seen  in  Table  6. 

TABLE  6 


Head  .  . 
Speed 

237  ft. 
1,700  r.p  m 

118.5  ft. 
1  200  r  p  m 

Discharge  

0.4  sec.  ft. 

0.4  sec.  ft. 

Bearing  friction 

1  20  h  p. 

0  72  h.p. 

Disk  friction  
Leakage  loss 

3.  00  h.p. 
2  00  h.p. 

1.06  h.p. 
0.71  h.p. 

Hydraulic  friction  

2.40h.p. 

1.20  h.p. 

Total  losses  

8.  60  h.p. 

3.69  h.p. 

Water  horse-power  

10.  70  h.p. 

5.35  h.p. 

Brake  horse-power  
Gross  efficiency  

19.  30  h.p. 
0.555 

9.04  h.p. 
0.592 

This  table  shows  that  for  the  lower  head  the  efficiency  is 
somewhat  higher.  If  the  rotative  speed  had  been  left  unchanged 
and  the  diameter  reduced  to  obtain  the  same  rate  of  discharge 
we  should  have  obtained  a  still  more  favorable  result  for  the 
"type"  of  the  impeller  would  have  been  smaller. 

The  curves  in  Fig.  85  indicate  that  the  efficiency  tends  to 
decrease  as  the  head  becomes  higher.  This  is  often  offset,  how- 
ever, by  the  fact  that  the  discharge  under  a  high  head  is  also 
large.  As  has  been  shown,  this  would  improve  the  efficiency. 
The  curves  indicate  that  the  greater  number  of  volute  pumps  are 
used  for  heads  per  stage  of  150  ft.  or  less,  while  with  turbine 
pumps  many  of  them  run  up  to  200  ft.  per  stage  or  more. 

Some  values  off  the  scale  are:  For  turbine  pumps,  heads  of 
498.6  ft.  and  863  ft.  showed  efficiencies  of  81  per  cent,  and 
60  per  cent,  respectively.  For  a  volute  pump  an  efficiency  of 
60  per  cent,  was  reached  under  a  head  of  700  ft. 

Taking  these  extensions  into  consideration,  the  curves  indi- 
cate that  good  efficiencies  may  be  obtained  even  though  the 
head  per  stage  be  high. 

79.  Efficiency — Speed. — In  order  to  vary  the  speed  of  a  series 
of  pumps  for  a  given  head  and  discharge,  it  would  be  necessary 
to  reduce  the  diameter  and  increase  the  width  as  the  speed  is 
increased.  This  would  result  in  reducing  the  value  of  the  ratio 


FACTORS  AFFECTING  EFFICIENCY 


119 


D/B,  which  has  already  been  considered  in  Art.  76.  We  should 
thus  see  that  increasing  the  rotative  speed  of  a  pump  for  a  given 
head  and  discharge  would  tend  to  improve  the  efficiency. 

It  would  be  possible  to  illustrate  this  case  with  a  tabular 
analysis  as  in  the  preceding,  but  it  is  hardly  worth  while.  The 
reason  for  the  change  in  efficiency  is  that  the  disk  friction  is 
much  less  for  the  smaller  diameter  of  impeller  running  at  the 
higher  speed. 

For  a  given  diameter  of  impeller  the  speed  for  a  fixed  head 
may  also  be  varied  by  changing  the  impeller  vane  angle  and 
thus  changing  <f>.  But  if  the  speed  is  reduced  by  this  method, 
so  as  to  reduce  disk  friction  and  bearing  friction,  the  hydraulic 
losses  tend  to  become  greater,  owing  to  the  difficulty  of  trans- 
forming the  kinetic  energy  into  pressure  energy. 

80.  Efficiency— G.P.M./Vh.— The  factor  G.P.M./y/h  is  a 
very  useful  factor  in  the  classification  of  centrifugal  pumps.  By 


100200       300       400       500       600       700       800       900      1000      1100     1200 
Turbine  Pumps.     G.  P.  M.  4- V/h  Per  Stage. 

FIG.  86. 


G.P.M.  is  meant  the  rate  of  discharge  in  gallons  per  min.  at  which 
the  efficiency  is  a  maximum  and  h  is  the  corresponding  head  per 
stage.  It  may  be  perceived  that  the  value  of  this  factor  is  con- 
stant for  a  given  impeller  regardless  of  the  actual  speed,  head,  and 
discharge  under  which  it  may  be  run,  providing  the  head  and 
discharge  are  the  best  for  that  speed. 

We  have  seen  that  the  tendency  is  for  the  efficiency  to  increase 
with  the  capacity  of  the  pump  and  to  decrease  with  the  head. 
Thus  we  may  represent  the  efficiency  as  a  function  of  the  ratio 


120 


CENTRIFUGAL  PUMPS 


of  G.P.M./\/h.  We  should  thus  assume  that  good  efficiencies 
might  be  obtained  even  under  very  high  heads  per  stage  if  the 
discharge  were  large  enough  to  give  us  a  reasonably  high  value 
of  this  factor. 

Average  curves  of  efficiency  against  this  factor  may  be  seen 
in  Figs.  86  and  87.  It  may  be  seen  that  higher  values  of  the 
ratio  are  found  with  the  volute  type  of  pump.  There  were 
numerous  values  that  were  off  the  scale  of  the  curves.  For  the 
turbine  pump  an  efficiency  of  81  per  cent,  was  had  with  a  value 
of  1,280.  For  volute  pumps  we  have  values  of  2,320,  3,290,  3,660, 
6,770, 7,700, 39,800,  and  44,400  with  efficiencies  of  80.0,  86.0,  66.0, 
82.0,  72.0,  77.5,  and  65.0  per  cent,  respectively. 


S50 

o 

|  40 
W30 


0    100200300400500600700800  90010001100120013001400150016001700180019002000 
Volute  Pumps,      G.  P.  M.  -4-  h  per  Stage. 

FIG.  87. 

81.  Efficiency — Specific  Speed. — Specific  speed  will  be  here 
merely  defined  as  N\/G.P.M./K*'*,*  where  h  =  the  head  per  stage. 
The  derivation  of  this  expression  and  its  meaning  will  be  given  in 
Art.  102.  This  factor  is  seen  to  involve  all  of  the  three  variables  of 
which  the  efficiency  is  a  function.  It  will  also  be  found  to  involve 
the  "type"  of  the  impeller.  It  will  be  constant  in  value  not  only 
for  a  single  impeller  at  any  speed  but  for  a  whole  series  of  im- 
pellers of  homologous  design,  such  that  each  impeller  is  merely 
an  enlargement  or  reduction  of  another,  possessing  the  same  pro- 
portions and  angles. 

Efficiency  curves  against  specific  speed  are  seen  in  Figs.  88 
and  89.  It  may  be  seen  that  the  volute  pumps  tend  to  higher 
specific  speeds  than  the  turbine  pumps.  It  must  be  borne  in 
mind  that  a  large  impeller  and  a  small  impeller  of  the  same 

*  Values  of  this  power  of  h  may  be  conveniently  found  on  the  slide  rule 
by  noting  that 

A3/*  =  h  +  tiA  =  h  -r  VVh 
See  table  in  Appendix  C. 


FACTORS  AFFECTING  EFFICIENCY 


121 


homologous  series  will  have  the  same  value  of  Ns,  but  we  should 
not  expect  their  efficiencies  to  be  identical'.  Thus  these  curves 
merely  show  the  general  tendency  of  this  factor  to  affect  the 
efficiency  without  enabling  us  to  pick  absolute  values.  Thus 
with  the  turbine  pumps  a  specific  speed  of  1,000  would  give  us 
a  range  of  efficiencies  from  50  to  80,  'depending  upon  the  actual 


^'"** 

fe 

—  ^ 

°~H 

—  — 





—._ 

0/oo 

o     ^ 

"•:,; 

°        0 

—  •— 

"—  —  ^ 

•  . 

^ 

--,. 

/ 

0^ 

?/ 

s 

f 

— 

—  -, 

^ 

^ 

/ 

OOU^ 

Y 

°/ 

' 

/ 

V 

/ 

0     200   400    600   800  100012001400  1600 1800  200022002400 2GOO  2800  3000  3200  34003600 
Turbine  Pumps     Specific  Speed  Ns_  Nyo.P.M. 

FIG.  88. — Efficiency  as  a  function  of  specific  speed. 

capacity  of  the  pump.  But  of  two  pumps  of  identical  capacities, 
for  example,  one  having  a  specific  speed  of  1,600  might  be  ex- 
pected to  have  a  better  efficiency  than  one  whose  specific  speed 
was  800. 

82.  Pumps  with  High  Specific  Speeds. — It  may  be  seen  that 
low  values  of  specific  speed  are  obtained  with  impellers  for  which 
the  ratio  D/B  is  large,  as  such  an  impeller  will  have  either  a  low 


0  400  800  1200  1(500  2000  2400  2800  3200  3000  4000  4400  4800  5200  6600  6000  6400  6800  7200  7600  8000 

Volute  Pumps,     Specific  Speed,      N.  =  y^^M' 

FIG.  89.  —  Efficiency  as  a  function  of  specific  speed. 


rotative  speed  or  a  low  discharge  for  a  given  head.  But,  as  has 
been  shown  in  Art.  76,  such  pumps  are  undesirable  from  the 
standpoint  of  efficiency.  The  curves  in  Figs.  88  and  89  also 
show  that  low  efficiencies  are  to  be  expected  with  very  small 
values  of  the  specific  speed.  Therefore  there  is  no  effort  made  to 
produce  pumps  with  low  specific  speeds. 


122 


CENTRIFUGAL  PUMPS 


But  an  effort  is  being  made  to  produce  centrifugal  pumps 
with  high  specific  speeds  as  such  pumps  are  desirable  for  con- 
nection to  steam  turbines  and  high-speed  motors.  It  may  be 
seen  that,  if  the  capacity  is  large  and  the  head  low,  a  very  high 
value  of  the  specific  speed  would  be  necessary  unless  the  rotative 
speed  is  very  low.  Such  a  combination  is  often  required  in  pumps 
for  supplying  condensing  water  and  similar  services.  We  might 
conclude  that  the  higher  the  specific  speed,  the  higher  the  effi- 
ciency, but  such  is  not  the  case  as  the  curves  in  Figs.  88  and  89 
will  show.  The  reason  is  that  after  we  pass  a  certain  point  it  is 


FIG.  90. — Centrifugal  pump  with  a  helicoidal  impeller.      (McEwen  Bros.) 

necessary  to  sacrifice  certain  desirable  features  in  design  in  order 
to  increase  the  capacity  of  an  impeller  without  increasing  its 
diameter  and  hence  reducing  the  speed.  But  the  value  of  a  high 
rotative  speed  with  a  large  discharge  under  a  low  head  is  often 
such  as  to  permit  some  sacrifice  of  efficiency. 

It  may  be  seen  that  to  increase  the  specific  speed  of  an  im- 
peller we  may  change  the  impeller  vane  angle  and  we  may  also 
decrease  the  value  of  the  ratio  D/B.  But  this  obviously  must 
have  some  physical  limit  since  the  diameter  of  the  eye  of  the 
impeller  must  be  less  than  D  with  the  usual  construction  and  a 
certain  minimum  area  of  the  impeller  eye  is  required  for  a  given 
rate  of  discharge.  For  this  reason  double  suction  impellers  may 


FACTORS  AFFECTING  EFFICIENCY 


123 


have  much  smaller  values  of  the  ratio  D/B  than  single  suction 
impellers  and  consequently  higher  specific  speeds. 

In  an  effort  to  produce  a  high-speed  pump  the  helicoidal  im- 
peller shown  in  Fig.  90  has  been  developed.1  The  small  size  of 
the  complete  pump  may  be  seen  in  Fig.  91.  By  this  form  of 
construction  the  entire  diameter  of  the  impeller  is  available  for 
the  admission  of  water  or  is  equivalent  to  the  eye  of  the  ordinary 


FIG.  91. — Steam  turbine  driven  pump  with  helicoidal  impeller. 
(McEwen  Bros.) 

impeller.  An  8-in.  pump  of  this  type  with  an  impeller  6  in.  in 
diameter  delivered  1,200  G.PM.  against  a  head  of  47  ft.  at  a 
speed  of  3,100  r.p.m.  A  30-in.  pump  with  an  impeller  of  18  in. 
diameter  delivered  24,000  G.P.M.  under  a  head  of  43  ft.  at  a 
speed  of  1,500  r.p.m.  The  specific  speeds  were  5,980  and  13,850 
respectively.  The  efficiencies  were  61  and  66  per  cent,  respect- 
ively. While  these  values  are  a  little  low  yet  it  must  be  borne 
in  mind  that  for  direct  connection  to  steam  turbines,  the  greater 
steam  economy  of  the  turbine  under  the  higher  speeds  will  com- 
pensate for  this. 

1  C.   V.   Kerr,    "A  New   Centrifugal  Pump  with   Helicoidal   Impeller," 
Journal  A.S.M.E.,  Vol.  35,  p.  1495,  Oct.  1913. 


124 


CENTRIFUGAL  PUMPS 


Since  the  capacity  of  the  usual  type  of  impeller  for  a  fixed 
rotative  speed  and  head  is  limited,  the  conditions  of  a  large 
discharge  under  a  low  head  are  sometimes  met  by  the  multi- 
impeller  type  of  pump  shown  in  Fig.  92.  With  this  construc- 
tion we  have  two  or  more  impellers  mounted  within  the  same  case 
so  that  the  total  capacity  is  divided  up  among  them.  This  makes 
it  possible  for  the  pump  as  a  whole  to  have  a  higher  value  of  the 
specific  speed  than  would  be  possible  with  a  single  impeller. 

83.  Effect  of  Number  of  Stages. — With  a  multi-stage  pump 
the  velocity  of  the  water  passing  from  one  stage  to  the  other 
is  kept  high.  This  eliminates  the  losses  that  inevitably  re- 


FIG.  92. — Multi-impeller  centrifugal  pump. 
Condenser  Co.) 


(Alberger  Pump  and 


suit  when  the  velocity  is  reduced.  Thus  the  loss  between 
stages  is  less  than  the  loss  that  accompanies  the  transforma- 
tion of  kinetic  energy  into  pressure  at  discharge  from  the  last 
impeller  into  the  case.  Therefore  the  efficiency  of  the  inter- 
mediate staged  is  higher  than  that  of  the  last  stage.  But  the 
efficiency  of  the  last  stage  is  practically  that  of  a  single-stage 
pump.  From  this  it  follows  that  the  efficiency  of  a  single-stage 
pump  is  less  than  that  of  a  multi-stage  pump  with  the  same 
speed,  discharge,  and  head  per  stage.  Also  it  may  be  seen  that 
the  efficiency  is  higher  the  greater  the  number  of  stages,  pro- 
viding always  that  the  speed  and  head  per  stage  is  the  same. 

In  the  preceding  paragraph  the  rotative  speed  and  head  per 
stage  were  the  same  for  all  cases  and  the  total  head  developed 
by  the  pump  varied  as  the  number  of  stages.  We  shall  now 
consider  the  more  usual  case  where  the  capacity  and  the  total 


FACTORS  AFFECTING  EFFICIENCY  125 

head  is  fixed  and  the  head  per  stage  and  the  rotative  speed 
may  be  varied  according  to  the  number  of  stages  employed. 
This  case  can  be  settled  only  by  a  consideration  of  the  specific 
speed,  N\/G.P.M./ti*.  The  curves  in  Figs.  88  and  89  show 
that  a  certain  range  of  values  of  specific  speed  is  conducive 
to  favorable  efficiency.  We  shall  thus  divide  the  total  head 
up  among  the  proper  number  of  stages  to  get  the  best  value  of 
specific  speed,  if  high  efficiency  be  our  primary  object.  In  any 
event  we  can  determine  the  relative  merits  of  different  numbers 
of  stages  by  computing  values  of  specific  speed  and  comparing 
with  the  average  curves  shown. 

Increasing  the  number  of  stages  for  a  given  capacity  and 
total  head  results  in  a  higher  value  of  the  specific  speed.  Thus 
where  the  capacity  is  small  and  the  total  head  is  high  a  multi- 
stage pump  is  more  desirable  than  a  single-stage  pump.  But 
for  the  case  where  the  capacity  is  large  and  the  head  very  low 
the  specific  speed  must  necessarily  be  high  even  for  a  single 
stage.  If  the  specific  speed  is  excessively  large  the  only  remedy 
is  to  resort  to  some  special  type  of  pump  as  in  Art.  82  or  to 
divide  the  water  among  several  pumps.  The  latter  is  what  the 
multi-impeller  pump  does. 

84.  Summary. — For  a  single  centrifugal  pump  the  maximum 
efficiency  possible  is  not  quite  independent  of  the  speed  but 
increases  as  the  speed  increases.  However,  after  a  certain  value 
of  the  speed  is  reached,  the  efficiency  will  begin  to  decrease. — 

For  a  series  of  centrifugal  pumps  the  efficiency  will  be  higher 
as  the  capacity  of  the  pump  is  greater,  providing  other  condi- 
tions are  favorable. 

The  efficiency  of  centrifugal  pumps  increases  as  the  head  be- 
comes less,  the  capacity  remaining  the  same.  This  statement  is 
true  only  within  certain  limits. 

For  a  given  head  and  discharge  the  efficiency  is  greater  as 
the  rotative  speed  is  greater  up  to  a  certain  limit.  This  is  be- 
cause the  "type"  of  the  impeller  is  becoming  smaller  in  value. 
But  after  a  certain  point  desirable  features  of  design  must  be 
sacrificed  in  order  to  secure  the  higher  speed. 

The  variation  of  efficiency  for  different  pumps  may  be  more 
properly  represented  as  a  function  of  the  factor  G.P.M./\/h 
or  the  factor  N\/'G7P~M'./h^J  where  h  is  the  head  per  stage. 
The  curves  in  Figs.  86,  87,  88,  and  89  will  enable  us  to  properly 
interpret  the  above  statements  and  to  roughly  fix  the  limits 


126  CENTRIFUGAL  PUMPS 

between  which  they  are  true.  Efficiency  may  be  sacrificed  by 
employing  pumps  for  which  these  factors  are  either  too  high  or 
too  low.  Thus,  although  in  general  the  efficiency  of  a  pump 
increases  as  the  capacity  increases,  if  the  speed  and  head  are  not 
suitable  the  efficiency  may  suffer,  since  the  specific  speed  may 
not  have  a  suitable  value. 

We  thus  see  that  a  favorable  efficiency  may  be  had  even  with 
pumps  of  small  capacity  providing  the  speed  is  sufficiently  high 
and  the  head  sufficiently  low.  But  a  much  better  efficiency  may 
be  had  for  a  large  capacity  pump  with  the  same  specific  speed. 
But  to  obtain  that  it  is  necessary  that  the  speed  should  be  rela- 
tively low  and  the  head  moderately  high.  To  obtain  a  large 
capacity  at  a  high  speed  under  a  low  head  involves  difficulties 
that  can  be  met  only  by  certain  special  constructions  and  the 
efficiency  is  not  likely  to  be  as  high  as  for  smaller  capacities 
under  the  same  conditions.  The  centrifugal  pump  is  not 
adapted  to  delivering  small  quantities  under  high  heads,  but  a 
good  efficiency  may  be  had  under  a  high  head  provided  the 
capacity  is  also  large. 

In  all  of  this  discussion  we  are  concerned  with  the  head  de- 
veloped by  a  single  impeller,  not  the  total  head  developed  by 
a  multi-stage  pump.  If  the  value  of  specific  speed  is  not  favor- 
able to  good  efficiency,  we  may  sometimes  improve  the  condi- 
tions by  dividing  up  the  total  head  into  various  numbers  of 


85.  PROBLEMS 

1.  At  800  r.p.m.  the  mechanical  efficiency  of  a  certain  centrifugal  pump  is 
90  per  cent.     If  the  total  mechanical  losses  (bearing  friction  and  disk  fric- 
tion) vary  as  the  square  of  the  speed,  what  is  the  mechanical  efficiency  at 
1,600  r.p.m.? 

Ans.  0.948. 

2.  If  the  gross  efficiency  of  the  pump  in  (1)  is  72  per  cent,  at  800  r.p.m., 
what  will  it  be  at  1*600  r.p.m.? 

Ans.  0.758. 

3.  If  the  capacity  of  the  pump  in  Table  5  had  been  6.00  cu.  ft.  per  sec., 
what  would  its  gross  efficiency  have  been? 

4.  A  pump  is  desired  to  deliver  500  G.P.M.  against  a  head  of  150  ft. 
Will  a  single-stage  or  a  2-stage  pump  give  a  better  efficiency? 

5.  How  many  stages  are  necessary  for  the  best  efficiency  to  be  obtained 
with  a  pump  to  deliver  2,000  GP.M.  against  a  head  of  600  ft.? 

Ans.  6  stages. 


FACTORS  AFFECTING  EFFICIENCY  127 

6.  If  a  pump  is  to  deliver  30,000  G.P.M.  at  a  head  of  100  ft.,  will  a  better 
efficiency  be  obtained  with  1  or  2  stages? 

7.  Would  a  better  efficiency  be  obtained  with  a  single  impeller  or  with 
two  impellers  in  parallel  for  a  discharge  of  30,000  G.P.M.  under  a  head 
of  100  ft. 

8.  It  is  desired  to  deliver  220  G.P.M.  against  a  head  of  40Q  ft.  at  3,600 
r.p.m.     What  will  be  the  values  of  the  specific  speed  for  1  stage  and  for 
2  stages? 

Ans.  597  and  1,000  respectively. 

9.  Which  will  give1  the  better  efficiency  in  (8)? 

10.  How  many  stages  would  be  necessary  in  (8)  for  a  specific  speed  of 
about  2,000?     Would  this  be  desirable? 

Ans*  5  stages. 

11.  A  single-stage  single-impeller  pump  delivers  6,700  G.P.M.   at  a  head 
of  60  ft.  when  running  at  1,140  r.p.m.     Would  there  be  any  gain  in  efficiency 
by  making  this  a  2-stage  pump  on  the  one  hand  or  by  dividing  the  discharge 
between  two  impellers,  the  rotative  speed  being  the  same? 

12.  If  it  were  desired  to  deliver  6,700  G.P.M.  at  60  ft.  head  at  3,000  r.p.m., 
what  type  of  pump  would  be  used? 

13.  The  efficiency  of  a  single-stage  centrifugal  pump  delivering  1,200 
G.P.M.  against  a  head  of  100  ft.  at  1,500  r.p.m.  is  70  per  cent.     Would  the 
efficiency  of  a  6-stage  pump  delivering  1,200  G.P.M.  against  a  head  of  600 
ft.  at  1,500  r.p.m.  be  any  greater  or  less  than  70  per  cent.? 


CHAPTER  IX 
CENTRIFUGAL  PUMPS  VS.  DISPLACEMENT  PUMPS 

86.  Relative  Speeds. — As  a  general  proposition  displacement 
pumps  must  run  at  slower  rotative  speeds  than  centrifugal  pumps. 
In  the  days  of  the  slow-speed  steam  engine  the  former  was  there- 
fore more  suitable  for  the  prime  movers  then  in  use.     But  with 
the  introduction  of  the  electric  motor  and  the  small  high-speed 
steam  turbine  the  displacement  pump  proved  to  be  less  suitable 
for  the  conditions  than  the  centrifugal  pump. 

87.  Comparative  Size. — For  the  same  service  the  centrifugal 
pump  will  be  much  smaller  than  the  reciprocating  pump.     Due 
to  its  higher  speed  the  motor  or  prime  mover  may  also  be  much 
smaller  in  size.     The  only  exception  to  this  would  be  for  a  pump 
handling  a  small  quantity  of  water  against  a  high  head.     In  such 
event  the  size  of  the  two  types  would  be  about  the  same,  in  fact 
for  an  extreme  case  the  displacement  pump  might  be  smaller. 

88.  Comparative  Efficiency. — For  the  conditions  to  which  the 
centrifugal  pump  is  adapted  it  is  probable  that  its  efficiency  will 
be  as  high  as  that  of  the  displacement  pump,  for  the  same  con- 
ditions.    This  will  be  especially  true  after  some  length  of  service 
as  the  efficiency  of  the  centrifugal  pump  will  not  deteriorate  as 
rapidly  as  that  of  the  displacement  pump.     In  other  cases  that 
are  unfavorable  to  the  efficiency  of  the  centrifugal  pump  it 
may  still  prove  to  be  true  that  it  is  preferable  on  account  of  over- 
whelming advantages  in  regard  to  characteristics,  cost,  size,  and 
other  factors. 

Also  when  the  economy  of  the  pump  and  motor  are  considered 
together,  the  overall  efficiency  will  be  more  likely  to  be  better 
for  the  direct-connected  centrifugal  pump  than  for  the  slower 
speed  reciprocating  pump  with  intervening  gearing  or  belt  drive. 
An  exception  to  this  statement  might  be  found  in  the  case  of 
large  pumping  engines.  For  such  units  the  slow-speed  steam 
engines  direct  connected  to  displacement  pumps  will  be  found  to 

128 


CENTRIFUGAL  PUMPS  VS.  DISPLACEMENT  PUMPS  129 


give  a  greater  steam  economy.     Whether  this  is  of  value  or  not 
depends  upon  the  relative  values  of  the  first  costs. 

89.  Comparative  Cost. — The  cost  of  a  centrifugal  pump  will  be 
less  than  that  of  a  displacement  pump  except  for  the  case  of  a 
very  small  capacity.  In  general  its  cost  may  be  said  to  be  about 
one-third  that  of  the  displacement  pump  for  high  lifts  and  less 
than  one-third  for  low  lifts.  Some  figures  that  were  compiled 
for  a  few  cases  are  given  in  Table  7. 

TABLE  71 


G.P.M. 

Head,  ft. 

Centrifugal  pump  and 
motor 

Reciprocating  pump  and 
motor 

H.p.                     Cost 

H.p. 

Cost 

167 

750 

60 

$1,365 

55 

$2,480 

300 

400 

52 

875 

55 

2,340 

300 

100 

14 

535 

20 

1,510 

700 

607 

190 

1,900 

180 

7,980 

When  the  total  cost  of  pumping,  which  includes  interest  on 
investment,  is  considered  it  may  be  found  that  the  centrifugal 
pump  will  be  more  economical  even  though  its  efficiency  might 
happen  to  be  lower. 

90.  Comparative  Characteristics. — If  a  centrifugal  pump  is  run 
at  a  constant  speed  the  amount  of  water  discharged  varies  as  some 
function  of  the  head.  It  is  possible  to  shut  off  the  flow  of  water 
entirely  without  causing  the  pressure  to  rise  above  a  certain 
With  a  displacement  pump  it  is  quite  different.  Neglecting  the 
variation  in  the  slip  under  various  heads,  the  rate  of  discharge 
for  a  displacement  pump  must  always  be  the  same  for  a  constant 
speed  regardless  of  the  head.  If  the  discharge  valve  is  closed 
the  pump  will  be  stopped  or  something  will  burst.  If  the  pump 
is  stopped,  the  pressure  obtained  will  depend  upon  the  maximum 
force  that  the  prime  mover  is  capable  of  exerting  on  the  water 
piston. 

For  the  centrifugal  pump  to  work  efficiently  under  various  heads 
it  is  necessary  to  vary  the  speed  of  the  pump  in  direct  proportion 
to  the  square  root  of  the  head.  The  normal  capacity  of  the  pump 
is  also  affected  when  the  speed  is  varied. 

With  the  displacement  pump,  on  the  other  hand,  there  is  no 
relation  between  head  and  discharge.  The  head  that  the  pump 

1  Proc.  of  Inst.  of  Mech.  Eng.,  1912,  page  7. 
o 


130  CENTRIFUGAL  PUMPS 

is  capable  of  working  under  depends  solely  upon  the  strength  of 
its  construction  and  the  power  of  the  prime  mover  to  operate 
its  piston  against  the  pressure  applied.  The  speed  has  nothing 
to  do  with  the  head.  In  fact  the  pump  may  maintain  pressure 
when  it  is  not  moving.  But  the  capacity  of  a  displacement 
pump  varies  directly  as  its  speed. 

91.  Advantages  of  Centrifugal  Pumps. — The  centrifugal  pump 
has  the  great  advantage  over  reciprocating  pumps  of  simplicity, 
reliability  and  ease  of  operation.     It  is  apt  to  be  much  more 
durable  than  the  displacement  pump,  especially  if  the  water  con- 
tains sand  or  grit.     The  centrifugal  pump  is  able  to  handle  water 
containing  sand  or  gravel  and  even  fair-sized  rocks,  an  impossi- 
bility for  the  other  type  of  pump. 

Another  important  feature  is  that  the  discharge  is  smooth 
and  continuous  and  free  from  the  shock  and  pulsations  that  are 
encountered  with  the  reciprocating  pump.  Since  the  pump  is 
more  free  from  vibrations  itself,  it  does  not  require  as  substantial 
foundations. 

It  has  already  been  pointed  out  that  the  centrifugal  pump 
usually  possesses  the  merits  of  a  higher  speed,  occupying  less 
space,  being  lighter  in  weight,  and  costing  less.  The  fact  that 
the  discharge  from  the  pump  may  be  shut  off  by  merely  closing 
a  valve  in  the  discharge  pipe  without  dangerous  pressures  being 
produced  or  requiring  the  motor  to  be  shut  down  is  often  of  great 
value. 

The  overall  efficiency  of  a  centrifugal  pump  set  is  often  better 
than  that  of  a  reciprocating  pump  set.  Even  in  cases  where  the 
efficiency  is  less,  the  cost  of  pumping,  when  interest  on  the 
investment  is  considered,  may  not  be  as  much  as  for  the  dis- 
placement type. 

92.  Advantages    of    Displacement    Pumps. — Kor    very    high 
heads,  especially  where  the  capacity  is  small,  the  displacement 
pumps  have  all  the  advantages  in  their  favor.     For  other  situa- 
tions they  may  have  a  greater  economy  in  some  instances.     Also 
they  are  able  to  lift  water  from  below  them  at  starting  without 
being  primed.     The  fact  that  there  is  no  relation  between  head 
and  discharge  is  often  an  advantage  in  their  favor.     Where  either 
the  head  or  the  discharge  are  required  to  vary  within  wide  limits 
and  where  they  do  not  maintain  definite  relations  with  each  other, 
the  displacement  pump  will  be  found  to  be  more  flexible  and 
more  economical. 


CENTRIFUGAL  PUMPS  VS.  DISPLACEMENT  PUMPS  131 

93.  PROBLEMS 

1.  Where  a  pump  is  required  to  supply  water  to  a  boiler  under  a  constant 
pressure  of  200  Ib.  per  sq.  in.  and  the  rate  of  pumping  will  vary  from  30 
to  50  G.P.M.  which  type  of  pump  is  more  suitable,  the  displacement  or  the 
centrifugal?     Why? 

2.  If  a  pump  is  required  to  supply  a  constant  amount  of  water  while  the 
head  may  vary  from  10  ft.  to  80  ft.  which  type  of  pump  is  more  suitable? 


CHAPTER  X 


COMPARISON  OF  TYPES  OF  CENTRIFUGAL  PUMPS 

94.  Maximum  Efficiency  of  Turbine  vs.  Volute  Pumps. — It 

is  usually  stated  that  the  volute  pump  is  very  good  for  low  heads 
but  is  inefficient  under  high  heads  and  that  for  the  latter  we 
should  resort  to  the  turbine  pump.  The  reason  why  the  value 
of  the  head  enters  the  question  is  thatJt-is  noooDGary-.to.  trans- 
form a  greater  per  cent,  of  the  kinetic  energy  of  the  water  leaving 
the  impeller  into  pressure  with  high  heads  than  with  low  heads. 
It  is  never  all  converted  into  pressure  because  the  water  must 
possess  a  certain  amount  of  kinetic  energy  as  it  flows  away  from 


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Percent  of  Normal  Discharge 

FIG.  93. — Efficiency  curves  of  various  types  of  centrifugal  pumps. 

the  case  into  the  discharge  pipe.  Since  the  difference  between 
the  two  pumps  is  in  the  method  of  converting  this  energy  and 
since  it  is  held  that  the  turbine  pump  can  do  it  more  efficiently, 
the  above  statement  is  made. 

The  various  efficiency  curves  in  Chapter  VIII  do  not  show  any 
material  differences  between  the  efficiencies  attained  with  turbine 
and  volute  pumps.  Heads  of  300  and  even  500  ft.  per  stage  are 
sometimes  found  with  volute  pumps  and  the  accompanying 
efficiencies  are  usually  as  good  as  one  would  have  reason  to 

132 


COMPARISON  OF  TYPES  OF  CENTRIFUGAL  PUMPS  133 

expect.     In  Fig.  93  the  volute  pumps  for  the  most  part  appear  to 
attain  slightly  higher  efficiencies  than  the  turbine  pumps. 

The  safe  conclusion  to  draw  from  the  evidence  at  hand  would 
be  that  there  is  ^^j^frrkpH  Hi>ffftrftn^ft  between,  the  maximum 
efficiencies  of  the  two  types  of  centrifugal  pump.  With  properly 
proportioned  volute  passages  it  may  be  possible  to  attain  as  good 
results  with  the  volute  pump  as  with  the  turbine  pump.  The 
fact  that  such  has  not  been  the  case  in  past  experience  may  be 
attributed  to  the  failure  of  designers  to  grasp  the  correct  solu- 
tion since  the  volute  is  not  so  amenable  to  mathematical  analysis 
as  are  diffusion  vanes. 

In  view  of  the  marked  superiority  of  volute  pumps  in  regard 
to  size,  simplicity,  and  cheapness,  it  is  evident  that,  when  their 
design  is  perfected,  they  will  be  more  widely  used  for  high-grade 
installations. 

It  should  be  noted,  however,  that  the  general  tendency  of 
practice,  as  shown  by  the  points  plotted  on  the  various  diagrams 
of  Chapter  VIII,  is  to  use  the  volute  pump  for  the  lower  heads 
and  at  higher  speeds,  in  other  words  with  higher  values  of  the 
specific  speed.  As  has  been  pointed  out,  that  alone  is  conducive 
to  improved  efficiency.  Thus  what- the  volute  lacks,  if  anything, 
in  regard  to  the  conversion  of  the  velocity  head  at  exit  from  the 
impeller,  it  may  make  up  to  some  extent  by  being  generally 
designed  for  more  favorable  values  of  specific  speed.  The 
curves  in  Chapter  VIII  would,  therefore,  appear  to  indicate  that 
for  certain  conditions  the  turbine  pump  would  have  a  higher 
efficiency  while  for  other  conditions  the  volute  pump  would  be 
superior. 

95.  Average  Efficiency  of  Turbine  vs.  Volute  Pumps. — It  has 
been  stated  that  the  efficiency  curve  of  the  volute  pump  will  be 
flatter  than  that  of  the  turbine  pump.  Thus  the  average  operat- 
ing efficiency  may  be  as  good  even  though  the  maximum  efficiency 
is  less.  The  curves  in  Fig.  93  will  not  bear  out  this  contention. 
The  efficiency  curves  here  are  generally  a  little  flatter  in  the 
case  of  the  turbine  pumps. 

It  would  require  a  great  deal  of  data  to  prove  this  point  to 
be  true.  Such  data  are  difficult  to  procure  as  the  pumps  should 
not  differ  widely  in  other  respects.  The  only  safe  conclusion 
to  draw  from  the  evidence  presented  is  that  there  4s  very  little,, 
difference  either  in  the  maximum  efficiencies  or  the  average 
efficiencies  of  turbine  and  volute  pumps. 


134  CENTRIFUGAL  PUMPS 

96.  Rising  vs.  Falling  Characteristics. — Since  the  water 
horse-power  for  a  pump  with  a  rising  characteristic  will  increase 
at  a  more  rapid  rate  as  the  discharge  increases  than  for  a  pump 
with  a  falling  characteristic,  it  would  be  expected  that  the  brake 
horse-power  should  also  increase  at  a  faster  rate.  Therefore, 
11  a  flaLJjrake  horse-power  curve  is  desired,  one  should  select 
a_pump  with  a  steep  falling  characteristic. 

A  pump  with  a  steep  falling  characteristic  will  probably  be 
better  for  service  under  conditions  where  the  static  head  is  apt 
to  vary  quite  widely,  while  the  speed  of  the  pump  is  kept  con- 
stant. Such  cases  might  be  found  with  a  dry-dock  pump  or  a 
condenser  circulating  pump  drawing  water  from  a  stream  whose 
level^fluct  uated . 

A  pump  with  a  rising  characteristic  is  considered  better  for 
service  where  the  vertical  lift  is  constant  and  where  there  is 
considerable  friction  head.  When  the  pump  is  run  at  constant 
speed  the  head  developed  by  the  pump  will  then  conform  some- 
what better  to  the  demands  of  the  lift  than  would  be  the  case 
otherwise.  It  may  be  seen  that  for  small  discharges  less  throt- 
tling would  be  required  than  for  a  pump  with  a  steep  falling 
characteristic.  (See  Fig.  76.) 

So  far  as  the  actual  efficiency  of  the  pump  itself  is  concerned, 
there  seems  to  be  no  systematic  variation  in  efficiency  between 
pumps  with  rising  and  falling  characteristics.  This  would  seem 
to  show  that  the  value  of  h"  dropped  as  rapidly  as  the  value  of 
h.  As  to  whether  a  rising  or  a  falling  characteristic  is  secured  is 
solely  a  question  of  the  vane  angle  and  the  number  of  vanes. 

97.  PROBLEMS 

1.  From  the  various  curves  in  Chapter  VIII  how  do  turbine  and  volute 
pumps  compare  as  to  efficiency  for  various  capacities?     For  various  heads? 

2.  What  are  apparently  the  best  values  of  G.P.M. /Vh  for  turbine  and 
volute  pumps  respectively? 

3.  What  are  apparently  the  best  values  of  specific  speed  for  turbine  and 
volute  pumps  respectively? 

4.  If  a  pump  is  required  to  deliver  500  G.P.M.  against  a  head  of  100  ft. 
would  a  turbine  or  a  volute  pump  apparently  be  better? 

6.  If  a  pump  is  required  to  deliver  10,000  G.P.M.  against  a  head  of  100 
ft.  what  type  of  pump  would  be  better,  the  turbine  or  the  volute? 

6.  A  2-stage  pump  is  required  to  deliver  1,000  G.P.M.  under  a  head 
of  250  ft.  at  1,400  r.p.m.  Would  a  turbine  or  a  volute  pump  be  better? 


COMPARISON  OF  TYPES  OF  CENTRIFUGAL  PUMPS  135 

7.  A  single-stage  pump  is  to  deliver  5,400  G.P.M.  against  a  head  of   130 
ft.  at  1,600  r.p.m.     Would  a  turbine  or  a  volute  pump  give  a  better  efficiency  ? 

8.  A  pump  is  required  to  deliver  5,000  G.P.M.  approximately  under  a 
head  which  may  range  from  15  ft.  to  25  ft.     Would  a  rising  or  a  falling 
characteristic  be  more  desirable? 

9.  A  pump  is  required  to  deliver  water  against,  a  constant  static  head  of 
60  ft.  through  a  long  pipe  line.     If  the  rate  of  flow  is  to  vary  from  3,000 
to  5,000  G.P.M.,  would  a  rising  or  a  falling  characteristic  be  more  desirable? 


CHAPTER  XI 

GENERAL  LAWS  AND  FACTORS 

98.  General  Relations. — In  the  theory  in  Chapter  V  we  have 
introduced  the  factors  <£  and  c  such  that  u%  =  <t>\/'2gh  and  vz 
=  c\/2gh.  These  may  also  be  rewritten  as  h  =  (\/<!>2)u2*/2g 
and  vz  =  (c/0)w2.  It  was  also  shown  that  for  any  single  pump 
a  certain  definite  value  for  0  and  also  for  c  was  necessary 
for  the  maximum  efficiency  to  be  obtained,  the  exact  values  of 
</>  and  c,  however,  depending  upon  the  design  of  the  particular 
pump.  But  since  these  values  are  fixed  and  constant  for  any 
single  pump  it  follows  from  the  above  that  for  the  condition  of 
maximum  efficiency  the  speed  and  discharge  of  the  pump  should 
vary  as  the  square  root  of  the  head,  the  water  horse-power  vary- 
ing as  the  three-halves  power  of  the  head.  It  has  been  shown 
that  the  efficiency  will  not  remain  absolutely  constant  under 
these  conditions,  therefore  the  brake  horse-power  does  not  vary 
in  quite  the  same  ratio  as  the  water  horse-power.  Also  for  the 
condition  of  maximum  efficiency  the  rate  of  discharge  will  vary 
as  the  first  power  of  the  speed,  the  head  as  the  square  of  the 
speed,  and  the  water  horse-power  as  the  cube  of  the  speed. 
The  brake  horse-power  will  not  vary  at  the  same  rate  as  the 
water  horse-power  for  the  reasons  shown  elsewhere. 

As  a  matter  of  fact  the  above  relations  need  not  be  restricted 
to  the  case  of  maximum  efficiency,  but  in  applying  these  laws  it 
is  only  necessary  that  $  and  c  shall  be  constant.  It  is  not  nec- 
essary for  them  to  be  the  best  values.  For  moderate  ranges  of 
speed  the  change  in  the  gross  efficiencies  will  be  slight.  There- 
fore a  constant  value  of  <£  (and  c)  means  an  approximately  con- 
stant efficiency.  Thus  in  Fig.  94,  assuming  that  0  and  c  have  the 
same  values  for  the  points  A,  B,  and  C,  it  will  be  found  that  these 
three  points  are  related  in  the  manner  given  by  the  laws  stated 
in  the  preceding  paragraph. 

Emphasis  should  be  laid  upon  the  fact  that  these  relations  may 
be  applied  only  to  points  for  which  </>  and  c  are  the  same,  such  as 
A,  B,  and  C.  It  is  frequently  stated  that  the  head  developed  by 

136 


GENERAL  LAWS  AND  FACTORS 


137 


a  centrifugal  pump  varies  as  the  square  of  the  speed  without  its 
being  recognized  that  the  rate  of  discharge  must  vary  at  the  same 
time,  if  such  a  law  is  to  apply.  If  any  one  of  the  three  factors 
of  speed,  head,  or-  discharge  is  to  remain  constant  or  vary  in 
some  way  so  that  0  and  c  cannot  remain  constant  in  value  for 
a  given  pump,  it  is  impossible  to  express  the  resulting  relations 
in  any  simple  way.  For  such  a  case  equations  (43)  and  (44) 
must  be  applied.  The  actual  relations  determined  by  test  may 
be  seen  in  the  curves  of  Chapter  VI. 


0      200     400     600     800    1000   1200   1400    1600    1800   2000   2200 
Water  Capacity,  Gallons  per  Minute 

FIG.  94. 

If  the  subscript  d)  denotes  values  under  1  ft.  head  we  may 
have  for  constant  </>  and  c  and  approximately  constant  efficiency: 

N  =  NiVh  (66) 

q  =  qiVh  (67) 

W.h.p.  =  (w.h.p.)  !/*3/2*  (68) 

If  the  prime  (')  denotes  values  at  1  r.p.m.  we  may  have  for 
constant  </>  and  c  and  approximately  constant  efficiency: 

q  =  q'N  (69) 

h  =  h'N*  (70) 

W.h.p.  =  (w.h.p.)W3  (71) 

99.  Values  of  <£  and  c  for  Maximum  Efficiency. — In  practically 
all  the  work  in  this  chapter  we  shall  be  concerned  only  with 
the  values  of  the  various  factors  for  which  the  gross  efficiency  is 
a  maximum.  It  will  thus  be  understood  that,  without  any 

*  For  convenience  with  the  slide-rule  it  may  be  noted  that  h3/* 


138  CENTRIFUGAL  PUMPS 

further  qualification,  all  values  of  constants  and  values  of  head, 
speed,  or  discharge  will  be  those  for  which  the  efficiency  is  a 
maximum  under  the  conditions.  (The  rated  head  and  capacity 
or  normal  head  and  capacity  of  a  pump  will  be  the  values  for 
which  the  efficiency  is  a  maximum  for  any  given  speed.  The 
maximum  efficiency  of  which  the  pump  is  capable  may  be  found 
at  some  other  speed,  however.  If  no  speed  is  specified  the  values 
will  be  those  at  the  speed  for  which  the  absolute  maximum  effi- 
ciency is  found.  Thus  for  the  pump  in  Fig.  72  we  should  say 
that  the  normal  head  and  discharge  are  237  ft.  and  0.4  cu.  ft. 
per  sec.  at  1,700  r.p.m.  But  if  1,000  r.p.m.  had  been  specified 
we  should  then  say  that  the  normal  head  and  "discharge  were 
80  ft.  and  0.23  cu.  ft.  per  sec.  respectively.) 

When  using  any  of  the  factors  given  in  this  chapter  the  value 
of  h  should  be  the  head  per  stage  in  the  case  of  a  multi-stage 
pump. 

For  purposes  of  design  the  value  of  (c  sin  #2)  is  often  more 
useful  than  the  value  of  c  alone.  It  is  therefore  given  below. 
With  many  designs  the  value  of  0  for  the  maximum  efficiency  is 
usually  not  far  from  unity,  but  the  following  range  may  actually 
be  found  : 

<t>  =  0.90  to  1.30 

c  =  0.10  to  0.30 

c  sin  0,2  =  0.05  to  0.15 

100.  Values  of  the  Ratio  D/B.— The  points  plotted  in  Fig.  80 
show  values  ranging  from  13.0  to  69.0.     Double  suction  volute 
impellers  for  very  high  specific  speeds  may  have  even  smaller 
values  than  this.     It  is  probable  that  the  maximum  range  that 
may  be  expected  is 

D/B  =  2  to  70 

101.  Impeller  Diameter  and  Discharge. — The  rate  of  discharge 
is  not  only  proportional  to  the  head  developed  but  also  to  the 
outlet  area  of  the  impeller.     The  latter  will  vary  with  the  design 
but  for  a  series  of  homologous  impellers,  all  alike  in  every  re- 
spect save  in  question  of  size,  the  proportions  and  angles  being 
the  same,  the  area  will  vary  with  the  square  of  the  diameter. 
We  may  thus  write 

G.P.M.  =  K^Vh  (72) 

For  a  series  of  homologous  impellers  the  value  of  Ki  would 
be  approximately  the  same  for  all  of  them.  As  there  would  be 


GENERAL  LAWS  AND  FACTORS  139 

slight  differences  in  finish  and  workmanship  the  results  from 
impellers  of  the  same  patterns  might  not  always  be  identical. 
Also  in  a  series  of  all  sizes  there  would  be  slight  variations  with 
the  different  sizes  so  that  the  series  would  not  be  strictly  hom- 
ologous. Thus  there  would  be  a  slight  variation  in  the  value  of 
KI  for  a  series  of  impellers  of  the  same  general  design.  For 
impellers  of  different  designs  it  may  be  seen  that  small  values 
of  KI  are  obtained  with  large  values  of  D/B  and  vice  versa. 

For  some  purposes  it  may  be  useful  to  rewrite  equation  (72) 
as 

G.P.M.  =  X'iDW  (73) 

Average  values  of  these  factors  may  be  said  to  be: 

K!  =  0.09  to  4.50 
K'i  =  0.000045  to  0.00225 

102.  Specific    Speed.  —  Since    u2  =  <l>\/2gh    and    also    uz  = 
wDN/720,  it  may  be  seen  that 

0  =  0.000543  ~  (74) 


N  =    '  (75) 

Since  $  is  constant  for  a  series  of  homologous  impellers, 
if  follows  that  DN/\/h  is  constant.  This  is  often  very  useful, 
as  it  enables  us  to  predict  the  performance  of  any  impeller 
of  a  series  if  the  head  developed  by  any  one  under  a  given  speed 
is  known.  Values  of  DN/\/h  may  range  from  1,660  to  2,400. 

From  (75)  we  obtain 

D  = 

From  (72)  we  obtain 


Substituting  for  the  value  of  D  in  the  second  expression  we  have 


Letting  Ns  stand  for  the  constant   factors  (\/  Kl  1,8400)   and 
rearranging  we  have 

N,  _  *^r-M,  (76) 

*  To  find  this  power  of  h  on  the  slide-rule  note  that 

kH  =  h  +  h1/*  =  h  +  \/V^ 
See  table  in  Appendix  C. 


140  CENTRIFUGAL  PUMPS 

This  factor,  called  in  this  work  the  specific  speed,  will  be 
found  to  be  extremely  useful.  It  serves  as  an  index  of  the  type 
of  pump.1  Its  physical  meaning  may  be  seen  as  follows: 
If  the  head  be  reduced  to  1  ft.  we  have  .N8  =  Ni\/G.P.M. 
By  then  increasing  or  decreasing  the  diameter  of  the  impeller 
we  increase  or  decrease  the  capacity.  But  NI  always  changes  in 
an  inverse  ratio  so  that  the  product  of  the  two  is  constant  and 
equal  to  N8.  If  the  size  of  the  impeller  be  such  that  G.P.M. 
=  1.0,  then  N8  =  NI.  That  is,  the  specific  speed  is  the  actual 
r.p.m.  at  which  an  impeller  of  the  series  would  run  under  1 
ft.  head  if  it  were  of  such  a  diameter  as  to  discharge  1  gal. 
per  min.  under  those  conditions. 

The  physical  meaning  of  Ns,  however,  is  of  little  practical 
value.  The  important  thing  is  that  it  is  a  factor  involving 
the  essential  quantities  with  which  we  are  concerned  in  selecting 
a  centrifugal  pump.  The  average  curves  of  efficiencies  that  have 
already  been  given  indicate  that  a  certain  range  of  values  of 
specific  speed  is  more  favorable  to  efficiency  than  values  either 
above  or  below  that.  Thus  in  selecting  the  speed,  head  per  stage, 
or  other  conditions  we  may  determine  what  are  the  best  quanti- 
ties to  choose. 

Also  for  a  homologous  series  of  pumps  the  specific  speed  will 
have  the  same  value  for  all  the  impellers,  regardless  of  their 
actual  size.  Thus  if  the  conditions  that  are  given  for  the  pump 
fix  a  certain  value  of  N,t  it  is  easily  determined  whether  some 
certain  impeller  of  a  given  series  will  be  suitable  or  not. 

The  specific  speed  is  an  index  of  the  type  of  impeller.  Speed 
and  capacity  are  merely  relative  terms.  An  impeller  with  a 
high  rate  of  rotation  is  not  necessarily  a  high-speed  impeller 

1  A  similar  expression  is  given  by  Greene,  "Pumping  Machinery,"  but 
he  uses  q  instead  of  G.P.M.  It  is  believed  that  the  latter  will  be  more  useful 
in  the  formula,  since  pump  capacities  are  generally  given  in  gallons  per  min. 
It  may  be  seen  that  values  given  by  (76)  are  21.2  times  the  value  if  q  is  used. 

For  a  hydraulic  turbine  specific  speed  is  defined  as  N»  =  N\/h.p./h5//i. 
It  is  easily  seen  that  the  capacity  of  a  turbine  or  pump  is  also  a  measure  of 
its  power  and  that  there  is  a  fixed  relation  between  the  two.  The  expression 
involving  horse-power  is  more  useful  for  the  turbine,  since  hydraulic  turbines 
are  rated  according  to  horse-power.  For  the  centrifugal  pump  the  expres- 
sion given  will  be  found  to  be  of  greater  value,  since  pumps  are  rated  accord- 
ing to  their  capacities,  not  their  power. 

Other  names  applied  to  this  factor  for  turbines  are  characteristic  speed, 
unit  speed,  and  type  characteristic. 


GENERAL  LAWS  AND  FACTORS  141 

for  its  capacity  may  be  very  small  and  the  head  high.  We 
may  classify  an  impeller  as  a  high-speed  impeller  only  when 
its  actual  speed  is  high  as  compared  with  other  impellers  for 
the  same  capacity  under  the  same  head.  All  of  these  rela- 
tions are  covered  by  N\/G.P.M./h%.  A  high-speed  impeller 
will  have  a  high  value  of  Ns,  though  its  actual  r.p.m.  may  be 
low,  while  a  low-speed  impeller  will  have  a  low  value  of  N8, 
though  its  actual  r.p.m.  might  happen  to  be  high. 

For  an  impeller,  either  single  suction  or  double  suction,  values 
of  specific  speed  may  be  found  between  the  following  limits:1 

N.  =  500  to  8,000 

For  a  special  form  such  as  the  helicoidal  impeller  (Fig.  90) 
the  specific  speed  may  be  even  higher.  The  above  values  apply 
only  to  single-stage  single-impeller  pumps.  For  a  multi-im- 
peller pump  it  is  necessary  to  divide  the  total  pump  capacity 
by  the  number  of  impellers  to  obtain  the  proper  quantity  for 
use  in  the  formula.  Likewise  for  multi-stage  pumps  the  total 
head  should  be  divided  by  the  number  of  stages  to  obtain  the 
value  of  h  to  be  used  in  (76). 

103.  Illustrations  of  Specific  Speed. — A  centrifugal  pump 
running  at  465  r.p.m.  delivers  16,780  G.P.M.  at  a  head  of  26 
ft.  The  specific  speed  is  5,240.  It  is  thus  a  high-speed  pump 
though  the  actual  r.p.m.  is  low. 

A  5-stage  centrifugal  pump  delivering  500  G.P.M.  at  a  head 
of  1,400  ft.  runs  at  3,000  r.p.m.  The  actual  speed  is  high  but 
the  specific  speed  being  only  980  shows  that  it  is  really  a  low- 
speed  pump.  That  is,  this  same  type  of  impeller,  if  it  were  to 
deliver  the  same  quantity  of  water  at  the  same  head  as  in  the 
preceding  example,  would  have  to  run  at  a  much  slower  speed 
than  the  465  r.p.m.  there  found. 

It  is  required  to  pump  20,000  G.P.M.  against  a  head  of  30  ft. 
at  1,700  r.p.m.  The  specific  speed  is  18,750  which  is  too  high 
for  a  single  pump.  It  would  be  necessary  to  reduce  the  speed 

1  If  it  is  desired  we  may  also  use  a  similar  factor  to  that  for  a  hydraulic 
turbine.  That  is,  N\^h/p./h^.  Its  derivation  is  similar  to  that  given  for 
(76).  For  w.h.p.  it  is  only  necessary  to  divide  the  values  given  by  (76)  by 
the  number  63.  Thus  N V w.h.p. /h^  varies  from  8  to  127.  If  b.h.p.  is 
used  assumptions  regarding  efficiency  are  necessary.  Inserting  certain 
values  of  efficiency  we  get  the  limits  to  be  10  and  140,  if  b.h.p.  is  used  in  the 
formula.  These  values  are  very  similar  to  those  found  with  hydraulic 
turbines.  See  the  author's  "Hydraulic  Turbines,"  page  104. 


142  CENTRIFUGAL  PUMPS 

for  a  single  pump  to  about  600  r.p.m.  or  to  divide  the  capacity 
up  among  six  impellers.  We  might  have  six  separate  independent 
pumps  running  at  1,700  r.p.m.  or  a  less  number  of  multi-impeller 
pumps. 

It  is  required  to  deliver  1,600  G.P.M.  at  a  head  of  900  ft.  with 
a  pump  speed  of  600  r.p.m.  For  a  single-stage  pump  this  would 
imply  the  impossible  specific  speed  of  146.3.  If  a  single-stage 
pump  is  used  its  speed  would  have  to  be  about  2,000  r.p.m.  at 
least.  If  a  speed  of  600  r.p.m.  is  necessary  the  pump  must  have 
at  least  six  stages.  This  would  give  a  specific  speed  of  560.  For 
a  better  efficiency  to  be  obtained  the  pump  might  be  divided  up 
into  12  stages.  This  would  give  a  specific  speed  of  940. 

An  impeller  8  in.  in  diameter  was  found  to  have  a  capacity 
of  900  G.P.M^  under  a  head  of  40  ft.  at  1,700  r.p.m.  This  would 
give  D  N/y/h  =  2,150,  K±  =  2.22,  and  Ns  =  3,200.  Suppose  a 
pump  was  required  to  deliver  3,000  G.P.M.  under  a  head  of  50 
ft.  at  1,100  r.p.m.  The  value  of  Ns  for  this  case  is  also  3,200. 
Therefore  an  impeller  of  exactly  the  same  design  as  the  first  one 
would  satisfy  the  requirements.  However  its  diameter  would 
have  to  be  13.8  in. 

104.  Determination  and  Use  of  Factors. — Values  of  all  the 
factors  given  in  this  chapter  can  be  computed  by  theory,  if  the 
essential  impeller  dimensions  are  known.  For  practical  use, 
however,  it  is  better  to  compute  them  from  test  data. 

The  uses  of  the  factors  have  already  been  indicated.  They 
serve  to  systematize  the  classification  of  centrifugal  pumps  and 
by  their  use  one  can  determine  the  limits  between  which  the 
choice  of  certain  conditions  for  a  centrifugal  pump  is  possible. 
By  their  aid  one  can  choose  more  wisely  and  with  greater  ease  the 
best  combination  of  speed,  discharge,  and  head  per  stage  for  given 
sets  of  conditions. 

105.  PROBLEMS 

1.  At  2,000  r.p.m.  a  centrifugal  pump  delivers  1,200  G.P.M.   at  a  head 
of  80  ft.     What  will  be  the  capacity  and  head  at  a  speed  of  1,000  r.p.m.? 
What  will  be  the  speed  and  discharge  for  a  head  of  60  ft.  ? 

2.  The  diameter    of   the   impellers    of    a    3-stage    pump    is    10   in.     At 
1,200  r.p.m.  the  pump  delivers  2,000  G.P.M.  at  300-ft.  head.     Find  values 
of  all  the  factors. 

3.  What  will  be  the  head  and  discharge  of  a   2-stage  pump  of  the  same 
type  as  in  problem  (2)  but  with  14-in.  impellers  if  the  speed  is  1,500  r.p.m.? 

4.  A  single  centrifugal  pump  under  a  head  of  26  ft.  will  deliver  16,000 
G.P.M.  when  running  at  460  r.p.m.     If  this  same  type  of  pump   is  used 


GENERAL  LAWS  AND  FACTORS  143 

under  this  head  but  the  total  capacity  is  divided  among  2,  4,  or  8  units, 
find  the  respective  speeds  that  will  be  attained. 

6.  What  would  be  the  necessary  r.p.m.  for  the  pump  in  problem  (4)  to 
have  a  specific  speed  of  3,000? 

6.  If  the  speed  of  the  pump  in  problem  (4)  were  kept  at  460  r.p.m., 
into  how  many  units  would  the  capacity  have  to  be  divided  to  give  a  specific 
speed  of  about  2,500? 

7.  It  is  required  to  deliver  1,600  G.P.M.  at  a  head  of  900  ft.  with  a  pump 
speed  of  1,500  r.p.m.     What  is  the  least  number  of  stages  that  would  be 
required?     How  many  stages  would  be  necessary  for  the  specific  speed  to 
be  about  2,500? 


CHAPTER  XII 
PUMP  TESTING 

106.  Purpose  of  Test. — Every  centrifugal  pump  should  be 
subjected  to  some  kind  of  a  test,  otherwise  the  purchaser  will  have 
little  assurance  that  the  guarantees  are  being  fulfilled.  Most 
builders  of  centrifugal  pumps  have  facilities  for  testing  in  their 
own  plants  and  test  every  pump  before  it  is  shipped.  If  desired, 
they  supply  the  purchaser  with  an  official  report  of  the  test. 
However  there  are  cases  where  the  makers  have  been  guilty  of 
certifying  a  pump  as  satisfactory  when  their  actual  test  has  shown 
it  to  be  very  deficient.  .  In  any  event  it  is  well  to  test  the  pump 
.after  it  is  installed,  if  it  is  feasible  to  do  so.  Also  a  repetition  of 
the  test  from  time  to  time  is  desirable  as  it  will  serve  to  indicate 
the  condition  of  the  pump. 

For  the  purpose  of  improving  pump  design,  a  large  amount 
of  testing  is  essential.  It  is  only  by  using  theory  and  actual 
test  results  together  that  improvements  or  radical  changes  can 
be  made.  The  successful  makers  of  centrifugal  pumps  base 
their  designs  upon  the  test  records  of  many  pumps. 

The  method  of  conducting  the  test  will  depend  upon  the  pur- 
pose for  which  the  test  is  to  be  made.  In  general  there  are  four 
main  purposes  as  follows : 

(a)  To  Determine  if  Guarantees  have  been  Fulfilled. — This  test 
will  usually  consist  of  determining  the  efficiency  or  the  duty,  as 
the  case  may  be,  of  the  pump  when  run  under  the  specified  con- 
ditions. At  the  same  time  it  will  be  established  whether  the 
specified  head  and  rate  of  discharge  can  be  obtained  simulta- 
neously under  the  specified  speed.  Such  a  test  involves  the 
determination  of  only  one  point.  In  some  cases  the  conditions 
may  be  specified  at  two  or  more  points. 

(6)  To  Determine  Characteristics. — Such  a  test  will  be  merely 
an  enlargement  of  (a).  A  sufficient  number  of  points  will  be 
determined  to  enable  curves  to  be  drawn.  In  fact  this  procedure 
is  the  most  satisfactory  way  of  testing  as  it  takes  but  little  more 
time  and  trouble  than  («),  complete  curves  are  more  desirable, 

144 


PUMP  TESTING  145 

and  also  the  appearance  of  the  curves  will  serve  to  indicate  the 
accuracy  of  the  test.  Usually  sucfi  a  test  as  this  will  be  run  with 
one  of  the  three  variables,  speed,  head,  or  discharge  constant. 
Of  these  the  speed  is  the  one  that  is  most  apt  to  be  kept  constant. 
The  resulting  curves  will  then  be  as  shown  in  Fig.  61.  From  such 
a  set  of  curves  it  is  possible,  by  using  the  principles  of  Art.  98, 
to  estimate  the  performance  under  any  other  conditions  of 
operation. 

(c)  To  Determine  General  Principles  of  Operation. — This  will  be 
similar  to  (6)  except  that  it  will  be  more  thorough  and  cover  a 
much  larger  number  of  points.     All  three  of  the  variables  of 
speed,  head,  and  discharge  will  be  varied  as  was  done  in  the  case 
of  the  Worthington  pump  in  Chapter  VI. 

(d)  To  Investigate  Fundamental  Principles. — This  test  will  be 
in  the  nature  of  research  and  will  be  of  interest  to  the  pump 
designer  or  to  one  who  is  making  a  thorough  study  of  the  sub- 
ject.    In  addition  to  the  regular  test  readings  a  number  of 
secondary  readings  might  be  taken  in  the  suction  pipe,  at  various, 
points  within  the  case,  or  between  the  diffusion  vanes  if  such  are 
used.     These  secondary  readings  might  be  to  determine  the  pres- 
sure, the  magnitude  of  the  velocity,  the  direction  of  the  velocity 
of  the  water,  or  other  phenomena.     They  could  be  secured  by 
pressure  gages  or  manometers,  Pitot  tubes,  vanes  which  would 
indicate  direction,  or  by  other  special  apparatus. 


107.  Measurement  of  Head. — To  measure  the  head  the  pres- 
sures should  be  determined  as  close  to  the  suction  and  discharge 
flanges  of  the  pump  as  possible  to  eliminate  pipe  losses  external 
to  the  pump.  The  pressure  on  the  discharge  side  may  be  read 
by  a  calibrated  pressure  gage  or  by  a  mercury  or  water  manometer 
if  the  head  is  low  enough.  On  the  suction  side  the  pressure  may 
be  read  by  a  vacuum  gage,  unless  the  water  is  under  positive 
pressure  at  this  point,  but  a  mercury  manometer  is  more  reliable 
and  is  simpler  and  cheaper,  since  the  reading  will  be  small.1 

In  making  connections  for  any  pressure  reading  it  should  be 

1  The  suction  gage  should  be  connected  as  shown  in  Fig.  95,  so  that  a 
pocket  of  air  cannot  collect  in  the  tube.  Unless  there  is  a  solid  column  of 
water  between  the  mercury  and  the  pipe,  the  manometer  reading  will  be 
incorrect.  If  it  were  known  that  there  was  no  water  at  all  in  the  tube  but 
that  it  was  entirely  filled  by  air,  it  would  then  be  known  that  the  manometer 
reading  was  the  value  of  ps  direct.  But  it  is  difficult  to  keep  all  the  water 
out  and  the  conditions  are  therefore  apt  to  be  unknown. 
10 


146 


CENTRIFUGAL  PUMPS 


borne  in  mind  that  the  tube  should  leave  the  pipe  at  right  angles 
to  the  direction  of  flow  and  that  the  end  of  the  tube  should  be 
flush  with  the  walls  of  the  pipe.  No  tube  which  projects  within 
the  pipe  will  give  a  true  pressure  reading,  even  though  the  orifice 
be  parallel  to  the  direction  of  flow  (or  the  tube  be  normal  to  the 
direction  of  flow).1 

In   computing  the  head,   equation   (12)  must  be  employed. 
That  is 

h  =  zd  -  z8  +  pd  -  ps  +  (Vd*  -  Vs*)/2g  (12) 

If  the  suction  and  discharge  pipes  are  of  the  same  size,  the  two 
velocity  heads  are  equal  and  cancel  each  other.  If  the  suction 


Pitot  Tube 


FIG.  95. — Measurement  of  head. 

and  discharge  flanges  are  at  the  same  elevation,  as  in  Fig.  95, 
Zd  —  zs  =  o.  But  under  other  circumstances  both  of  these 
items  should  be  considered. 

The  pressure  gage  in  Fig.  95  records  the  pressure  at  the  center 
of  the  gage,  not  at  (d).  Likewise  the  mercury  manometer  read- 
ing is  the  pressure  (below  the  atmosphere  or  suction)  at  the  top 
of  the  right-hand  mercury  column,  not  at  (s).  If  the  height  of 
the  pressure  gage  above  the  center  of  the  pipe  is  x  and  the  gage 
reads  P  Ib.  per  sq.  in. 

pd  =  2.308  X  P  +  x 

1  Hughes  and  Safford,  "Hydraulics,"  page  104. 


PUMP  TESTING  147 

If  the  suction  gage  reading  in  inches  of  mercury  is  S  and  the 
distance  from  the  top  of  the  right-hand  mercury  column  to  the 
center  of  the  pipe  is  y  —  x, 

ps  -  -1.1325  -  (y  -  x). 
Therefore 

pd  -  ps  =  2.308P  -f  1.1325  +  y 

If  the  water  at  entrance  to  the  pump  is  under  positive  pressure, 
we  should  have  ps  =  +1.1325  —  (y  —  x).  Thus  we  should 
have  pd  -  ps  =  2.308P  -  1.1325  +  y.  . 

Even  if  the  suction  and  discharge  flanges  of  the  pump  are  not 
at  the  same  elevation,  it  may  easily  be  shown  that  2.308P  ± 
1.1325  +  y  =  zd  —  za  +  pd  —  ps.  For  if  our  suction  and  dis- 
charge piping  in  Fig.  95  were  so  arranged  that  the  center  line  of 
the  pipe  passed  through  the  level  of  the  summit  of  the  right-hand 
mercury  column  and  through  the  level  of  the  center  of  the  pres- 
sure gage,  the  gages  remaining  in  their  present  positions,  the  gage 
readings  reduced  to  feet  of  water  would  be  the  values  of  ps  and 
Pd-  But  zd  —  za  would  then  be  y. 

Therefore  for  any  setting  whatever,  the  head  developed  by  a 
pump  will  be 

h  =  2.308P  +  1.1325  +  y  +  (Vd*  -  V82)/2g  (77) 

The  +  sign  should  be  used  for  5  whenever  the  reading  is  a 
vacuum  such  as  in  Fig.  95.  If  the  suction  pressure  is  greater 
than  that  of  the  atmosphere  th#-—  sign  should  be  used.  The 
above  formula  has  been  given  in  this  way  because  the  most  com- 
mon instruments  are  pressure  gages,  graduated  in  pounds  persq. 
in.  and  mercury  manometers.  The  essential  thing  is  that  the 
term  (2.308P)  should  represent  the  pressure  in  feet  of  the  liquid 
pumped,  recorded  at  the  center  of  the  gage  or  at  the  surface  of 
the  "well"  or  the  lower  column  of  a  U  tube  if  a  mercury  column 
is  used.  Likewise  the  term  (1.1325)  should  be  the  pressure  in 
feet  of  the  liquid  pumped,  read  by  the  suction  gage  or  other 
device. 

108.  Measurement  of  Water. — The  difficult  problem  in 
some  pump  testing  is  the  measurement  of  the  rate  of  discharge. 
The  means  that  may  be  employed  according  to  circumstances  are 
to  weigh  or  measure  the  volume  of  water  discharged  in  a  known 
time  interval,  to  use  a  weir,  a  Venturi  meter,  a  Pitot  tube, 
or  a  calibrated  nozzle.  In  some  instances  floats  or  current 


148  CENTRIFUGAL  PUMPS 

meters  have  been  used  in  the  channel  leading  water  to  or  away 
from  the  pump. 

To  measure  the  volume  of  or  weigh  the  water  discharged  in  a 
certain  time  interval  is  feasible  only  for  small  capacities,  save 
in  exceptional  circumstances  such  as  where  a  pump  is  to  deliver 
water  to  a  large  reservoir.  It  is  a  method  that  may  often  be 
found  in  laboratories. 

The  weir  is  a  standard  device  for  measuring  water  but  for  a 
large  capacity  the  expense  of  constructing  it  might  be  excessive. 
It  should  be  remembered  that  all  weir  formulas  and  coefficients 
are  purely  empirical  in  their  nature  and  that  the  different  formu- 
las that  are  accepted  at  large  do  not  yield  identical  results.  It 
is  therefore  necessary  to  select  the  formula  based  upon  actual 
experiments  upon  weirs,  whose  construction  and  proportions 
are  the  nearest  to  the  weir  used.  The  most  widely  used  weir 
formulas  are  the  Francis  and  the  Bazin  formulas.  The  Francis 
formula  slightly  modified  is 

q  =  3.33(L  -  0.1  nH)  (H  +  ah,)1-6 

where  L  is  the  length  of  the  weir  crest  in  feet,  H  is  the  head  on 
the  weir  measured  in  feet,  n  is  the  number  of  end  contractions 
or  is  zero  for  a  suppressed  weir,  hv  the  velocity  head  in  the  weir 
channel,  and  a  a  factor  varying  from  1.0  to  2.0  according  to 
circumstances.1  Experiments  of  Schoder  and  Turner  indicate 
that  for  H  =  0.1  ft.  the  factor  3.33  should  be  increased  by  7 
per  cent.,  for  H  =  0.2  ft.  by  3  per  cent.,  and  that  it  is  correct 
when  H  =  0.3  ft. 

For  small  rates  of  discharge  the  triangular  weir  is  better  than 
the  rectangular  weir.  Any  angle  of  notch  may  be  employed. 
For  the  90°  triangular  notch  the  formula  is 

q  =  2.54  H2-5 

The  Venturi  meter  is  very  satisfactory  and  should  be  perma- 
nently installed  in  many  pumping  plants  as  it  permits  of  the 
measurement  of  water  without  any  interference  in  its  flow. 
The  extra  friction  head  induced  by  it  is  very  small. 

The  Pitot  tube  may  be  used  to  measure  the  velocity  in  a 
closed  pipe  or  in  a  free  jet  as  in  Fig.  95.  The  impact  of  the 
stream  against  the  orifice  of  the  tube  produces  a  pressure  which 

1  R.  L.  Daugherty,  "Investigation  of  the  Performance  of  a  Reaction 
Turbine,"  Proc.  of  Am.  Soc.  of  C.  E.,  Oct.,  1914,  page  2482. 


PUMP  TESTING 


149 


I 
I 


150  CENTRIFUGAL  PUMPS 

is  proportional  to  the  square  of  the  velocity.  If  h  is  this  pressure 
reading  in  feet  of  water,  and  K  an  experimental  constant, 

V  =  K<^2gh 

The  value  of  K  is  often,  though  not  necessarily,  unity.  It 
is  affected  by  the  design  of  the  tube  and  the  manner  of  deter- 
mining h.  If  the  water  is  in  a  closed  pipe,  h  should  be  the 
difference  between  the  actual  Pitot  tube  reading  and  the 
pressure  head  in  the  pipe,  for  the  Pitot  tube  reading  will  be 
the  pressure  head  plus  the  velocity  head.  If  h  is  the  difference 
between  the  pressure  recorded  by  an  orifice  facing  the  stream 
and  another  orifice  in  another  tube  at  the  same  location  in  the 
stream  but  with  the  orifice  parallel  to  the  stream,  the  value  of  h 
will  not  be  the  same  as  in  the  former  case  for  the  reason  given 
on  page  146.  Again  h  may  be  the  difference  between  the 
pressures  recorded  by  two  tubes,  the  orifice  of  one  facing  up  the 
stream  and  the  other  facing  down  the  stream.  Such  an  in- 
strument is  called  a  pitometer  and  is  useful  for  low  velocities 
since  the  reading  is  magnified.  For  this  case  the  value  of  K 
is  always  less  than  unity.  In  using  the  Pitot  tube  for  any 
case  it  must  be  noted  that  the  velocity  is  not  uniform  across 
a  section  of  the  stream.  It  is,  therefore,  necessary  to  take 
readings  at  various  points  in  order  to  compute  the  total  discharge. 
For  a  free  jet  it  is  probably  true  that  the  maximum  velocity 
found  across  its  section  is  the  true  ideal  velocity  determined 
by  \/2gH  where  H  is  the  total  head  back  of  the  nozzle.  This 
affords  a  means  of  determining  the  constant  K. 

If  a  nozzle  has  been  calibrated  it  may  be  used  for  measuring 
the  rate  of  discharge  as  shown  in  Figs.  95  and  96.  It  is  necessary 
,to  measure  either  the  pressure  back  of  the  nozzle  or  the  velocity 
head  recorded  by  a  Pitot  tube  in  the  center  of  the  jet.  The 
rate  of  discharge  of  the  nozzle  will  be  known  as  a  function  of 
one  or  the  other  of  these  two  readings.1 

109.  Measurement  of  Speed. — The  most  satisfactory  way 
of  measuring  speed  is  by  means  of  a  reliable  and  sensitive  ta- 
chometer. This  will  serve  to  indicate  not  only  the  speed  at 
a  given  instant  but  show  if  the  speed  is  varying.  The  ta- 

1  For  useful  information  regarding  the  methods  of  measurement  here 
indicated  see  Hughes  and  Safford,  "Hydraulics,"  and  R.  E.  Horton,  "Weir 
Experiments,  Coefficients,  and  Formulas,"  U.S.G.S.  Water  Supply  and 
Irrigation  Paper  No.  150,  Revised,  No.  200. 


PUMP  TESTING  151 

chometer  should  be  calibrated  occasionally.  A  very  good  device 
for  measuring  speed  has  been  found  to  be  a  magneto  and  a 
voltmeter.  The  magneto  is  belted  to  the  pump  shaft  and  con- 
nected to  the  voltmeter.  After  calibration  it  will  serve  very 
nicely  for  a  tachometer.  By  the  choice  of  a  suitable  voltmeter 
scale  any  degree  of  accuracy  in  reading  may  be  attained  and  it 
will  also  be  sensitive  to  fluctuations  in  speed. 

Lacking  a  tachometer  a  revolution  counter  may  be  used  for 
determining  speed.  Care  should  be  exercised  in  its  use,  however, 
as  it  will  not  indicate  fluctuations  in  speed  and  also,  unless 
the  readings  are  extended  over  a  sufficient  time,  it  will  not 
give  an  accurate  average.  A  revolution  counter,  however,  is  a 
standard  in  itself  and  requires  no  calibration.  That  is  a  valu- 
able point  in  its  favor. 

110.  Measurement  of  Power. — For    a  testing  laboratory  a 
transmission  dynamometer  is  a  very  useful  device  for  measur- 
ing the  power  delivered  to  the  pump.     Lacking  this  the  motor  or 
prime  mover  may  be  calibrated  and  such  readings  taken  that  the 
brake  horse-power  (or  developed  horse-power)  may  be  known 
under  the  conditions  of  the  test.     The  power  output  of  the  motor 
or  prime  mover  is  the  power  input  to  the  pump. 

For  some  direct  connected  units  it  may  be  difficult  or  nearly 
impossible  to  determine  the  horse-power  delivered  to  the  pump. 
In  such  event  it  is  possible  to  determine  only  the  efficiency  of  the 
set. 

111.  Plotting  Curves. — In  plotting  curves  it  should  be  borne 
in  mind  that  any  single  point  may  be  in  error  but  that  all  of 
them  should  follow  a  definite  law,  unless  some  factor  is  intro- 
duced which  causes  an  abrupt  change  from  one  law  to  another. 
Therefore  smooth  curves  should  be  drawn  for  the  points  plotted. 
Also  for  a  series  of  curves  such  as  those  in  Fig.  77,  there  should 
be  a  certain  degree  of  uniformity  among  them.     This  often  helps 
to  decide  what  the  true  curve  probably  is,  when  the  test  points 
are  few  in  number  or  are  obviously  inaccurate. 

It  is  often  better  to  construct  such  curves  as  those  between 
head  and  rate  of  discharge  and  between  brake  horse-power  and 
rate  of  discharge  and  to  compute  the  efficiency  curve  from  values 
read  from  these  curves  rather  than  to  attempt  to  draw  efficiency 
curves  through  the  points  computed  direct  from  the  test  data. 


152  CENTRIFUGAL  PUMPS 


112.  PROBLEMS 

1.  In  a  pump  test  the  pressure  gage  read  50  Ib.  per  sq.  in.  and  the  suction 
gage  recorded  a  vacuum  of  10  in.  of  mercury.     The  center  of  the  pressure 
gage  was  2.0  ft.  above  the  center  of  the  pump  shaft  while  the  summit  of  the 
upper  mercury  column  of  the  manometer  was  1.0  ft.  below  the  center  of  the 
shaft.     The  suction  and  discharge  pipes  were  of  the  same  size.     What  was 
the  value  of  the  head? 

Ans.  129.7  ft. 

2.  In  a  pump  test  the  pressure  gage  read  100  Ib.  per  sq.  in.  while  the  suc- 
tion gage  recorded  a  positive  pressure  of  5  Ib.  per  sq.  in.     The  centers  of  the 
two  gages  were  at  the  same  level.     The  diameter  of  the  suction  pipe  was  3 
in.  and  that  of  the  discharge  pipe  2  in.     If  the  rate  of  discharge  was  100 
G.P.M.,  find  the  head  developed. 

Ans.  220.6  ft. 

3.  A  centrifugal  pump  is  equipped  with  mercury  manometers  for  measur- 
ing both  discharge  and  suction  pressures.     The  suction  and  discharge  pipes 
are  of  the  same  size.     If  the  pressure  reading  is  10  ft.  of  mercury  when  the 
summit  of  the  lower  column  is  4  ft.  below  the  center  of  the  pump  shaft  and 
the  suction  manometer  reads  10  in.  of  mercury  when  the  summit  of  the  upper 
column  is  1.0  ft.  below  the  center  of  the  pump  shaft,  what  is  the  value  of 
the  head? 

Ans.  144.2  ft. 


CHAPTER  XIII 


COSTS 

113.  Costs  of  Centrifugal  Pumps. — There  are  so  many  factors 
affecting  the  cost  of  a  centrifugal  pump  that  no  simple  rule  or 
set  of  curves  can  be  given  by  which  the  cost  of  a  pump  can  be 
determined.  For  any  given  capacity  the  cost  is  affected  by  the 
head  that  is  required,  by  the  speed  selected,  the  number  of  stages, 
the  quality  of  construction,  and  commercial  conditions. 

For  similar  conditions  of  head,  speed,  and  construction,  the 
cost  may  be  approximately  given  as  a  function  of  the  capacity. 
The  curves  in  Figs.  97  and  98  will  give  the  average  costs  of  some 


0  100  200  300  400  600  600  700  800.  900  1000 110012001300 14001600100017001800 

Oapacity'in  Gal.  per  Min. 

FIG.  97. — Cost  of  stock  centrifugal  pumps. 

single-stage  stock-pumps.  Curve  (A)  applies  to  very  cheaply 
constructed  pumps  for  low  heads.  The  impellers  are  of  iron 
and  are  single  suction.  The  pumps  are  belt  driven.  Curve 
(B)  is  for  pumps  similar  to  (A)  but  with  double-suction  impellers. 
The  lower  one  of  the  two  curves  shown  for  (B)  at  small  capacities 
is  for  belt-driven  pumps,  the  upper  one  for  pumps  arranged 
to  be  direct  connected  to  motors.  The  pumps  of  curve  (C) 
are  of  much  better  construction  than  the  preceding  and  are  suit- 
able for  heads  up  to  130  ft.  They  are  also  to  be  belt  driven. 

153 


154 


CENTRIFUGAL  PUMPS 


Curve  (D)  represents  fairly  good  construction  and  one  suited  for 
direct  connection  to  a  motor. 

All  of  the  pumps  for  which  these  curves  are  drawn  are  for 
moderate  heads  only  and  they  have  iron  impellers.  To  illustrate 
the  effect  of  the  construction  upon  the  cost,  Table  8  is  presented. 

TABLE  8. — COST  OF  A  G-IN.  PUMP 


Iron 

Brass 

Bronze 

Single  suction 

$200 

$360 

$475 

Double  suction  

350 

650 

785 

The  cost  of  a  2-stage  pump  is  about  three  times  the  cost  of 
a  single-stage  pump  for  the  same  discharge,  speed,  and  head  as 


2.000 
1.800 
1.600 
1.400 
1.200 
1.000 


400 


X5 


X 


X 


X 


rH        N        CO        T*        us*       to"        C-*      00        OS*       £        £       N        eg        j£       £ 

Capacity  in  Gal.  per  Min. 

FIG.  98. — Cost  of  stock  centrifugal  pumps. 

one  of  the  stages.  As  the  number  of  stages  is  increased  the  factor 
by  which  the  cost  of  a  single-stage  pump  must  be  multiplied 
will  approach  the  number  of  stages. 

When  pumps  for  high  heads  are  considered  it  will  be  seen  that 
the  curves  in  Figs.  97  and  98  are  entirely  inadequate.  A  few 
cases  to  illustrate  this  may  be  cited.  It  will  be  seen  that  there 
is  no  uniformity  among  these  few  cases  because  the  speeds, 
number  of  stages,  and  other  features  may  be  quite  different. 
A  centrifugal  pump  with  a  capacity  of  2,500  G.P.M.  under  600 
ft.  head  cost  $5,000.  Another  with  a  capacity  of  5,560  G.P.M. 
under  a  head  of  280  ft.  cost  $26,000,  while  a  third  with  a  capacity 
of  27,800  G.P.M.  under  300  ft.  head  cost  $55,000.  The  De  Laval 


COSTS  155 

Steam  Turbine  Co.  state  that  a  steam  turbine-driven  centrifugal 
pump  of  the  waterworks  type  for  200-ft.  head  will  cost  about 
$1,000  per  million  gallons  daily  capacity. 

The  quantity  that  is  the  most  nearly  constant  in  value  is 
the  cost  per  Ib.  For  a  number  of  small  iron  pumps  this 
seems  to  be  about  20  cents.  For  brass  or  bronze  it  will  be  higher. 
The  quality  of  construction  will  not  affect  this  very  much  be- 
cause better  construction  usually  requires  more  metal,  hence  the 
total  weight  is  greater.  As  the  size  of  the  pump  increases,  the 
cost  per  Ib.  will  become  less. 

114.  Cost  of  Pumping. — The  total  cost  of  pumping  is  the  sum 
of  the  fixed  charges  and  the  operating  expenses.  The  former 
consists  of  interest  on  the  capital  cost,  insurance,  taxes,  depre- 
ciation, and  administration.  The  latter  item  includes  labor,  fuel 
or  electric  current,  supplies,  repairs,  and  other  similar  items. 

The  capital  cost  covers  the  cost  of  the  pump,  motor  or  prime 
mover,  and  possibly  the  building,  pipe  lines,  and  such  other  equip- 
ment that  the  pumping  makes  essential. 

The  total  annual  cost  consists  of  fixed  charges  and  operating 
costs  for  a  period  of  1  year.  The  cost  of  pumping  per  water 
horse-power  or  per  1,000  gal.  per  min.,  or  any  similar  unit  is  the 
total  annual  cost  divided  by  the  total  capacity  of  the  pump, 
meaning  by  total  capacity  the  water  horse-power  or  the  number 
of  1,000  gal.  per  min.,  or  other  units  of  which  the  pump  is  capable^ 
It  will  be  a  minimum  when  the  pump  is  not  operated  at  all  as  it 
will  then  consist  of  the  fixed  charges  only.  It  will  be  a  maximum 
when  the  pump  is  operated  continuously  as  that  will  cause  the 
operating  expenses  to  be  a  maximum. 

For  a  steam-driven  pumping  unit  the  total  annual  cost  of 
pumping  is 

C  =  G  X  8-33pX  hXS  +  L+F(i  +  d  +  t)+M        (78) 

in  which 

C  =  total  annual  cost 

G  =  total  number  of  gallons  pumped  per  year 

h  =  head  in  feet 

S  =  cost  of  steam  per  1,000  Ib. 

D  =  duty  in  foot  pounds  per  1,000  Ib.  of  steam 

L  =  cost  of  labor  and  similar  items 

F  =  total  investment 

i  =  interest  rate  on  investment 


156  CENTRIFUGAL  PUMPS 

d    =  rate  of  depreciation 

t     =  taxes,  insurance,  etc. 

M  =  administration  and  similar  items. 

For  a  motor-driven  pump  we  should  have  to  consider  S  as 
meaning  the  cost  per  million  B.t.u.  supplied  to  the  motor, 
(1.0  k.w.  hr.  =  3,412  B.t.u.),  and  D  =  duty  in  ft.  Ib.  per  million 
B.t.u.,  supplied  to  the  motor.  From  equation  (24)  duty  = 
778,000,000  X  efficiency  of  set.  Therefore  the  first  part  of 
equation  (78),  if  K  =  cost  of  power  per  k.w.  hr.,  is 

G  X  8.33  XhXK 
2,655,000  X  set  efficiency 

Equation  (78)  shows  that,  if  the  cost  of  power  is  high,  it  may 
be  economical  to  pay  a  high  price  for  a  high-duty  pumping  engine. 
But  on  the  other  hand  a  less  expensive  centrifugal  pump  may 
often  effect  a  saving  even  though  its  duty  should  be  somewhat 
less.  Equation  (78)  would  also  show  that  for  intermittent  serv- 
ice a  cheap  pump  was  desirable  even  though  it  might  be  in- 
efficient. But  for  constant  service  a  high-duty  pump  is  better 
even  though  its  first  cost  may  be  considerably  higher. 

116.  PROBLEMS 

1.  The  City  of  Youngstown,  O.,  installed  a  turbine-driven  centrifugal 
pump  with  a  capacity  of  5,840  G.P.M.  at  a  head  of  276  ft.     (The  14-in. 
single-stage  pump  was  built  by  the  Wilson-Snyder  Centrifugal  Pump  Co. 
The  turbine  was  supplied  by  the  Kerr  Turbine  Co.)     The  maximum  duty 
determined  by  test  was  89,000,000  ft.  Ib.  per  1,000  Ib.  of  steam.     With 
coal  at  $1.95  per  ton  and  an  evaporation  of  8.5  Ib.  of  steam  per  Ib.  of  coal, 
the  cost  of  steam  per  1,000  Ib.  would  be  11.5  cents  or  $0.115.     The  total  cost 
of  the  installation  was  $10,000,  the  interest,  etc.,  on  which  will  be  taken 
as  14  per  cent.     Omitting  the  items  L  and  M,  what  is  the  total  cost  of  pump- 
ing per  year,  assuming  the  pump  to  run  continuously? 

Ans.  $10,530. 

2.  The   City  of  Youngstown  also  has  a  triple-expansion  reciprocating 
pumping  engine  for  practically  the  same  conditions  as  the  above.     The 
guaranteed  duty  is  163.000,000  ft.  Ib.  per  1,000  Ib.  of  steam  and  the  first 
cost  was  $72,000.     Assuming  interest,  etc.,  to  be  14  per  cent,  as  above  and 
adding  a  total  of  $400  for  cylinder  oil  and  valves,  find  the  total  annual  cost 
of  continuous  pumping  and  compare  with  (1).. 

Ans.  $15,480. 

3.  What  would  be  the  cost  of  coal  per  ton  that  would  make  the  total  costs 
of  pumping  equal  in  (1)  and  (2)? 

4.  What  would  have  to  be  the  cost  of  the  reciprocating  pumping  engine 


COSTS  157 

in  (2)  for  it  to  be  as  economical   as  the  turbine-driven  centrifugal  pump 
in  (1)? 

5.  What  would  have  to  be  the  per  cent,  of  interest,  etc.,  on  the  fixed 
charges  to  equalize  the  costs  of  pumping  in  (1)  and  (2)? 

6.  A  motor-driven  centrifugal  pump  with  an  efficiency  of   75  per  cent, 
delivers  l,OOGT(z.P.M .  during  2,660  hr.  per  year  at  a  head  of  150  ft.     If  the 
motor  efficiency  is  90  per  cent,  and  the  cost  of  power  is  $0.04  per  k.w..hr., 
find  the  annual  cost  of  power  for  the  unit. 

Ans.  $4,450.  j 

7.  If  the  above  pump  is  steam  driven  by  a  turbine  with  a  thermal  efficiency 
of  8  per  cent.,  what  will  be  the  duty?     If  steam  costs  $0.25  per  1,000  Ib. 
and  each  pound  possesses  1,050  B.t,.u.,  what  is  the  cost  of  power? 

Ans.  46,700,000  ft.  Ib.  per  million  B.t.u.,  or  49,000,000  ft.  Ib.  per  1,000 
Ib.  of  steam,  $1,020. 


CHAPTER  XIV 
ROTARY  AND  SCREW  PUMPS 

116.  Rotary  Pump. — This  type  of  pump  is  illustrated  here 
because  the  term  is  often  erroneously  understood  to  mean  a 
centrifugal  pump.  The  true  rotary  pump  is  a  positive  action 
displacement  pump.  Its  motion,  however,  is  one  of  rotation  and 
not  reciprocation.  One  form  of  this  pump  may  be  seen  in  Fig. 
99.  It  consists  of  a  pair  of  shafts  which  are  maintained  in  the 
same  relation  to  each  other  by  a  pair  of  spur  gears.  Within  the 
case  there  are  a  pair  of  lobe  gears  which  mesh  with  each  other 


FIG.  99.— The  rotary  pump.     (Goulds  Mfg.  Co.) 

and  are  so  arranged  that  water  is  admitted  to  the  space  between 
two  lobes  when  this  space  is  open  to  the  suction.  As  the  rotation 
continues  this  space  is  shut  off  from  communication  with  the  suc- 
tion and  the  water  is  carried  up  to  the  discharge  side.  As  the 
lobes  mesh  with  each  other  there  is  little  opportunity  for  the 
water  to  return  to  the  suction  side  save  by  leakage. 

This  type  of  pump  is  suitable  for  certain  classes  of  service 
under  low  head.     They  are  apt  to  be  noisy  and  inefficient  in 

158 


ROTARY  AND  SCREW  PUMPS  159 

operation.  As  they  are  continued  in  service  the  wear  is  sufficient 
to  permit  considerable  leakage  and  thus  the  economy  decreases.1 
117.  Screw  or  Propeller  Pump. — The  screw  or  propeller 
pump  is  analogous  to  the  centrifugal  pump  but  the  flow  of  the 
water  is  axial  rather  than  radial.  The  helicoidal  impeller 
(Fig.  90)  is  an  approach  to  the  screw  pump.  The  result  ob- 
tained with  the  helicoidal  impeller  is  the  ability  to  handle  a 
large  rate  of  discharge  at  a  low  head  with  a  high  rotative  speed 
as  has  already  been  shown.  The  same  thing  is  true  for  the 
screw  pump  and  to  a  greater  degree.  For  certain  purposes, 
such  as  are  implied  by  these  conditions,  these  pumps  are  useful. 
But  their  efficiency  is  generally  low. 

1  For  an  account  of  the  test  of  a  large  rotary  pump  having  a  good  effi- 
ciency see  "Test  of  a  Rotary  Pump,"  by  W.  B.  Gregory,  Trans.  A.S.M.E., 
Vol.  28,  page  963. 


CHAPTER  XV 
APPLICATIONS  OF  CENTRIFUGAL  PUMPS 

118.  Steam  Power  Plants. — The  centrifugal  pump  has  be- 
come practically  the  standard  type  for  circulating  the  condensing 
water.  The  combination  of  large  capacity  and  low  head  that 
is  usually  encountered  in  this  work  is  very  favorable  to  this  type 
of  pump.  Where  the  static  head  varies,  as  it  may  where  water 


FIG.  100. — Multi-stage  centrifugal  boiler  feed  pumps.     (Platt  Iron  Works.) 

is  being  pumped  from  a  river,  it  is  desirable  to  operate  the  pump 
under  a  variable  speed  for  the  sake  of  economy.  If  a  constant 
speed  is  preferred  because  of  its  simplicity,  the  pump  should 
possess  a  steep  characteristic,  in  order  that  the  fluctuations  of 

160 


APPLICATIONS  OF  CENTRIFUGAL  PUMPS       161 

head  should  not  greatly  alter  the  rate  of  discharge.  If  the 
static  head  is  constant  the  pump  should  possess  a  flat  or  a  rising 
characteristic  so  that  the  discharge  may  be  varied,  if  desired, 
without  great  loss  of  efficiency. 

The  centrifugal  pump  is  also  becoming  very  popular  for  a 
boiler  feed  pump.  Though  the  small  capacity  and  high  head  of 
such  a  pump  is  detrimental  to  efficiency,  that  is  of  small  con- 
sequence, if  the  pump  is  steam  turbine  driven,  since  the  exhaust 
steam  is  all  used  for  heating  boiler  feed  water.  However,  the 
steam  economy  of  such  a  unit  is  certainly  greater  than  that  of 


FIG.  101. — Two-stage  centrifugal  fire  pump.     (Platt  Iron  Works.) 

the  direct-acting  steam  pumps  that  are  often  employed  for  such 
a  purpose.  The  merits  of  the  centrifugal  pump  for  boiler  feed- 
ing are  found  in  its  operating  characteristics.  It  delivers  water 
smoothly  without  shock  or  pulsation. 

119.  Fire  Pumps. — The  centrifugal  pump  offers  many  at- 
tractive features  for  use  as  a  fire  pump,  on  account  of  its  re- 
liability and  comparatively  low  first  cost.  Since  a  pump  for 
fire  protection  is  used  but  a  small  portion  of  the  time,  the  question 
of  first  cost  and  reliability  outweighs  all  others.1  For  this 

1  See  "High-pressure  Fire  Service  Pumps  of  Manhattan  Borough"  by 
R.  C.  Carpenter,  Trans.  A.S.M.E.,  Vol.  31,  page  437  (1909). 
11 


162 


CENTRIFUGAL  PUMPS 


purpose  especially  rugged  construction  is  demanded  and,  where 
the  pump  is  motor  driven  as  in  Fig.  101,  a  shield  is  usually 
required  to  protect  the  motor  from  any  water  that  might  leak 
from  the  pump.  A  fire  pump  should  have  a  flat  characteristic. 


FIG.  102. — Vertical  shaft  pump.     (De  Laval  Steam  Turbine  Co.) 


120.  Deep  Well  Pumps. — For  deep  well  pumps  or  for  mine- 
sinking  pumps  the  vertical-shaft  centrifugal  pump  is  well  adapted 
as  it  occupies  but  little  space.  The  motor  may  be  mounted 
with  the  pump  for  mine  sinking  so  that  the  set  can  be  readily 
lowered  as  the  water  level  in  the  mine  shaft  falls. 


APPLICATIONS  OF  CENTRIFUGAL  PUMPS      163 


164 


CENTRIFUGAL  PUMPS 


121.  Mine  Pumps. — For  either  temporary  use  or  for  perma- 
nent installations  in  mines,  the  centrifugal  pump  offers  the 
great  advantages  of  small  size  -and  weight  and,  due  to  its  freedom 
from  vibration,  very  light  foundations  are  sufficient.  Most 
water  encountered  in  mine  pumping  is  corrosive  in  its  action, 
due  to  the  presence  of  various  acids.  This  corrosive  action  is 
more  detrimental  in  the  case  of  a  displacement  pump  than  in  the 
case  of  a  centrifugal  pump.  In  Fig.  103  is  shown  a  pump  for  use 
in  a  coal  mine,  where  considerable  sulfuric  acid  is  present.  This 


FIG.  104. — Six-stage  centrifugal  pumps  for  hydraulic  pressure  governors  of 
water  turbines.  Capacity  =  1100  G.P.M.,  h  =  461  ft.,  N  =  1170  r.p.m. 
(/.  P.  Morris  Co.) 

set  consists  of  two  single-stage  volute  pumps  connected  in  series. 
All  the  parts  which  come  in  contact  with  the  water  are  made  of 
special  acid  resisting  bronze.  The  pump  was,  therefore,  made  as 
simple  as  possible.  The  case,  head  covers,  and  suction  elbows 
are  all  split  on  a  horizontal  plane,  so  that  dismantling  for  in- 
spection or  repairs  is  readily  accomplished.  The  first  of  these 
pumps  has  now  been  in  service  5  years  and  shows  but  little 
deterioration  under  the  action  of  the  acid. 


APPLICATIONS  OF  CENTRIFUGAL  PUMPS       165 

122.  Dredging.— For  dredging  purposes  the  centrifugal  pump 
is  the  only  type  that  can  be  considered,  on  account  of  the  large 
solid  materials  that  have  to  be  handled.  Pumps  for  this  service 
are  rapidly  worn  out  and  the  cases  are  often  lined  with  steel  to 
resist  the  erosive  action  of  the  grit  and  gravel  that  is  thrown 
against  them.  Cheapness  in  first  cost,  ability  to  withstand 
abuse,  and  ease  of  repair  are  more  important  than  efficiency. 


FIG.  105. — Drainage  pump.     (Platt  Iron  Works.) 

123.  Waterworks. — In  large  waterworks  we  find  that  condi- 
tions of  steady  load  the  greater  part  of  the  year  render  it  eco- 
nomically possible  to  install  costly  pumping  machinery  with 
high  efficiencies.  For  such  service  the  triple-expansion  pumping 
engine  has  been  perfected  and  has  given  very  high  duties. 

The  speed  of  the  usual  large  reciprocating  engine  is  usually 
too  low  for  direct  connection  to  the  centrifugal  pump  and  the 
speed  of  the  steam  turbine  is  too  high,  since  the  waterworks  type 
of  centrifugal  pump  will  not  have  a  very  high  speed  owing  to  its 
large  capacity.  It  is  therefore  necessary  to  connect  the  turbine 
to  the  pump  by  means  of  reduction  gears  such  as  are  shown  in 


166 


CENTRIFUGAL  PUMPS 


Figs.  106  and  107.     This  is  the  most  desirable  arrangement  for 
using  a  centrifugal  pump  of  large  capacity. 

The  duty  of  the  steam  turbine-driven  centrifugal  pump  will 
not  be  as  high,  perhaps,  as  that  of  the  very  efficient  pumping 


FIG.  106. — Steam  turbine-driven  centrifugal  pump  for  waterworks. 
Capacity  =  6,950  G.P.M.,  h  =  200ft.,  N  =  1100  r.p.m.  Turbine  speed 
=  3600  r.p.m.  (Platt  Iron  Works.) 


FIG.  107. — Steam  turbine-driven  centrifugal  pump  for  waterworks. 
Capacity  =  71,260  G.P.M.,  h  =  58.7  ft.,  N  =  345  r.p.m.,  discharge 
=  48  inches.  (De  Laval  Steam  Turbine  Co.) 

engine.  But  its  lower  first  cost  may  enable  it  to  be  more  econom- 
ical than  the  pumping  engine,  as  is  shown  by  the  problems  in 
Art.  115.  This  is  not  always  the  case  as,  where  the  cost  of  fuel 
is  high,  the  high-duty  pumping  engine  may  give  a  greater  economy 
despite  its  greater  first  cost. 


APPLICATIONS  OF  CENTRIFUGAL  PUMPS       167 

In  comparing  the  capital  costs  of  the  two  types  of  pumping 
units,  it  is  well  to  note  that  the  turbine-driven  centrifugal  pump 
requires  less  room  than  the  triple-expansion  pumping  engine,  the 
foundations  may  be  much  lighter,  and  a  smaller  crane  need  be 
installed  to  handle  the  parts  of  the  machine.  This  means  a 
much  cheaper  building. 

In  comparing  operating  costs  it  must  be  noted  that,  though  the 
fuel  economy  of  the  pumping  engine  may  be  much  higher,  more 
labor  is  often  needed  to  attend  to  it  and  the  cost  of  cylinder  oil, 
renewing  valves,  and  other  repairs  is  greater.  Frequent  atten- 
tion is  also  needed,  otherwise  the  slip  will  become  excessive  so 
that  the  rated  duty  will  not  be  attained.  With  the  centrifugal 
pump  the  economy  will  change  very  slowly. 

The  pumping  engine  is  more  difficult  to  repair  in  case  of  a 
breakdown  than  the  centrifugal  pump.  All  of  these  factors 
tend  to  show  that  the  turbine-driven  centrifugal  pump  is  well 
worthy  of  consideration  for  waterworks  pumping  plants.  The 
choice  between  the  two  types  can  be  made  only  by  carefully 
estimating  all  the  separate  items  that  affect  the  result. 

124.  Miscellaneous  Uses. — The  preceding  classes  of  service 
are  typical  of  the  field  that  can  be  covered.  Thus  drainage  and 
irrigation  are  often  comparable  with  waterworks  service,  while 
sewage  pumping  requires  features  that  may  be  intermediate  be- 
tween this  and  dredging  work.  The  development  of  hydraulic 
pressure  for  elevators  and  similar  purposes  will  require  a  pump  of 
the  type  suitable  for  boiler  feed.  For  marine  use  the  merits  of 
the  centrifugal  pump  are  the  small  space  occupied,  the  light 
weight,  light  foundations  required,  and  freedom  from  vibration. 

For  handling  all  kinds  of  corrosive  liquids  and  material  which 
is  likely  to  clog  small  passages,  the  centrifugal  pump  is  better 
adapted  than  any  other  type. 


CHAPTER  XVI 
DESIGN  OF  A  CENTRIFUGAL  PUMP 

125.  Empirical  Procedure. — In  this  chapter  only  the  deter- 
mination of  such  dimensions  as  are  involved  in  the  hydraulics 
of  the  pump  will  be  considered.  The  design  of  mechanical  details 
such  as  bearings,  shafts,. and  other  features  will  not  be  treated, 
as  such  may  be  found  in  general  works  on  machine  design. 

Owing  to  the  inherent  defects  of  the  theory  of  the  centrifugal 
pump,  any  method  of  design  must  involve  the  use  of  empirical 
factors  determined  by  experience.  This  is  true  of  practically  all 
engineering  work,  but  in  some  cases  the  factors  are  reasonably 
constant  or  are  known  to  vary  as  definite  functions  of  other 
quantities.  The  determination  of  numerical  values  for  these 
factors  is  not  so  certain  in  the  case  of  the  centrifugal  pump. 

The  design  of  a  centrifugal  pump  impeller  is  ultimately  based 
upon  the  performances  of  other  impellers.  The  theory  indicates 
what  would  be  the  general  effect  of  altering  certain  dimensions. 
Hence  successful  design  consists  of  modifying  or  changing  the 
design  of  impellers  which  have  been  tested  out  rather  than  the 
creation  of  entirely  new  patterns.  After  a  number  of  impellers 
of  different  types  have  been  constructed  and  their  performances 
properly  recorded,  the  designer  will  then  be  in  a  position  to 
develop  new  designs  and  to  predict  results  with  some  assurance. 

As  an  illustration,  suppose  that  it  is  required  to  design  a 
centrifugal  pump  of  a  certain  capacity  under  a  given  head.  The 
number  of  stages  and  the  r.p.m.  might  be  arbitrarily  assumed 
for  non-technical  reasons.  But  more  scientifically  they  might 
be  determined  in  accordance  with  the  material  given  in  Chap- 
ter XIII,  due  regard  being  shown  commercial  conditions  at 
the  same  time.  But  it  is  seen  that  the  experimental  data  shown 
in  the  curves  of  Chapter  VIII  will  be  necessary  before  even  this 
much  can  be  done. 

Having  now  the  values  of  N,  G.P.M.,  and  h  per  stage,  the  de- 
sired form  of  impeller  characteristic  may  be  selected.  That  is 
we  may  decide  whether  a  rising,  a  flat,  or  a  steep  characteristic 
is  more  suitable  for  the  particular  work  this  pump  is  to  do. 

168 


DESIGN  OF  A  CENTRIFUGAL  PUMP  169 

Having  chosen  this,  it  will  be  necessary  to  select  the  angle  of 
the  impeller  vane  at  exit.  Again  experience  will  be  necessary 
for  this  to  be  done,  since  it  cannot  be  determined  by  the  solution 
of  any  mathematical  equation.  The  theory,  however,  indicates 
that  the  smaller  the  angle  a2  the  steeper  the  characteristic.  Ex- 
perience also  points  to  the  fact  that  the  fewer  the  number  of 
vanes  the  steeper  the  characteristic.  Also  the  theory  (or  more 
plainly  the  curves  in  Fig.  58)  will  show  that  the  angle  of  the  dif- 
fusion vanes  or  the  area  of  the  volute  case,  if  vanes  are  lacking, 
has  an  effect  upon  this.  The  larger  the  diffusion  vane  angle  A '2 
or  the  larger  the  case  of  a  volute  pump,  the  higher  the  discharge 
and  the  lower  the  head  at  which  the  maximum  efficiency  will  be 
found.  Only  by  the  study  of  the  performances  of  other  pumps 
for  which  these  quantities  are  known  can  the  proper  values 
of  e&2  and  A' 2  or  Fs  be  chosen. 

The  next  step  is  the  selection  of  the  factors  <f>  and  c,  whose  values 
may  normally  range  from  0.90  to  1.30  and  from  0.10  to  0.30 
respectively.  The  steeper  the  characteristic  the  larger  the  value 
of  0.  Therefore  0  is  some  function  of  the  quantities  in  the  pre- 
ceding paragraph,  as  is  c  also.  If  the  theory  were  capable  of 
exact  application,  we  might  compute  values  of  <f>  and  c  from  the 
equations  given  in  Chapter  V,  but  even  those  equations  involve 
the  selection  of  a  factor  k  which  is  a  matter  of  experience  again. 
We  shall,  therefore,  have  to  choose  a  value  for  <£  according  to 
our  best  judgment  or  according  to  values  obtained  by  test  upon 
a  pump  similar  in  design  to  the  one  we  are  attempting.  The 
value  of  c  may  be  determined  in  the  same  manner  as  </>. 

As  a  check  upon  the  rationality  of  our  values  of  oc2,  <£,  and  c 
we  may  substitute  them  in  equation  (50),  and  see  if  the  value 
of  the  expression  is  in  accordance  with  the  customary  values 
for  the  line  of  pumps  whose  data  we  may  have.  If  our 
theory  were  exact  the  value  of  (50)  would  be  the  true  hydraulic 
efficiency,  a  value  for  which  might  reasonably  be  estimated. 
As  our  theory  is  defective,  that  is,  since  the  computed  value  of 
In"  is  higher  than  the  true  value  as  shown  in  Figs.  58  and  59, 
this  value  will  not  be  any  definite  physical  quantity  and  is  called 
simply  "manometric  coefficient."1  Or  we  might  assume  a 

1  For  a  large  number  of  pumps  ranging  from  capacities  of  50  to  6,250 
G.P.M.  the  author  has  found  values  of  this  coefficient  ranging  from  0.543 
to  0.762  as  extremes,  though  the  usual  values  were  from  0.56  to  0.65.  The 
gross  efficiencies  in  most  cases  were  higher  than  these  values. 


170  CENTRIFUGAL  PUMPS 

value  of  the  "  manometric  coefficient"  and  compute  c  from  (50). 
With  values  of  <£  and  c  determined,  we  can  compute  the  essential 
impeller  dimensions  as  follows: 
From  (75) 

D  =  1,840  <t>Vh/N  (79) 

The  required  impeller  area  may  be  computed  as 
/2  =  q/vz  =  G.P.M./44S  c^2gh 

Combining  the  value  of  /2  given  by  equations  (3)  or  (4)  with  this 
we  obtain 

0.04  X  G.P.M. 

=  ~ 


or 

0.04  X  G.P.M. 


(irD  sin  a2  -  nt)  X 

We  should  employ  (80)  or  (81)  according  to  whether  we  have  used 
(3)  or  (4)  respectively  for  computing  values  of  /2,  in  order  to 
calculate  the  values  of  c  for  previous  pumps.  As  has  been  pointed 
out,  these  two  values  will  be  identical  if  the  vanes  are  involute 
curves.  (The  G.P.M.  here  used  should  also  include  the  esti- 
mated leakage  loss.) 

It  is  customary  to  make  the  diameter  of  the  vanes  at  entrance 
DI  equal  to  about  0.5Z),  though  this  ratio  may  vary  from  0.3 
to  0.6  or  even  extend  beyond  these  limits.  The  essential  thing 
is  to  see  that  the  eye  of  the  impeller  is  sufficiently  large  in  diame- 
ter so  that  cavitation  will  not  be  produced  due  to  too  high  a 
velocity  head  at  this  point  with  a  consequently  low  value  of 
pressure. 

The  width  of  the  impeller  at  entrance  BI  is  usually  from  1.0 
to  2.05.  For  a  given  DI  both  this  width  and  the  angle  a\  are 
usually  so  chosen  that  the  absolute  velocity  at  entrance  may  be 
radial  for  the  normal  rate  of  discharge.  Before  proceeding  further 
it  will  be  necessary  to  consider  the  suction  pipe.  A  size  will  be 
chosen  for  that  that  will  give  a  reasonable  velocity  of  flow  for 
a  given  suction  head.  By  properly  proportioning  the  intake  to 
the  pump  case  and  the  eye  of  the  impeller  it  will  be  possible  to 
gradually  accelerate  the  water  as  it  approaches  the  entrance  to 
the  impeller  vanes.  With  the  amount  of  acceleration  determined, 
we  can  compute  the  value  of  Vi,  since  the  velocity  in  the  suction 
pipe  has  been  chosen.  The  value  of  Vi  is  usually  not  much 
different  from  v2  sin  a2.  The  area  Fl  =  q/Vi  =  G.P.M.  /448  Vi. 


DESIGN  OF  A  CENTRIFUGAL  PUMP  171 

But  the  area  FI  =  (n-DiBi/14A)  —  vane  thickness.  Since  the 
velocity  diagram  at  entrance  is  a  right-angled  triangle  for  the  case 
of  radial  flow,  we  know  that  vt  sin  «i  =  Vi  and  v\  cos  oi  =  u\. 
Dividing  one  of  these  by  the  other  we  can  determine  the  angle 
since,  Vi  and  Ui  are  known.  Thus 

tan  «i  =  YI/UI  (82) 

The  essential  dimensions  of  the  impeller  are  thus  determined. 
If  the  results  lead  to  poor  proportions,  some  of  the  assumptions 
can  be  altered  and  new  solutions  found. 

If  we  wish  to  choose  the  diffusion  vane  angle  for  a  turbine 
pump  so  that  no  shock  loss  is  occasioned  at  this  speed  and  rate  of 
discharge  we  can  make  the  angle  A\  =  A%.  Therefore 

V2  sin  a-2  c  sin  0,% 

tan  A'2  =  -  -  =  -  (83) 

Uz  —  v2  cos  a2       (j>  —  c  cos  a2 

For  a  volute  pump  we  may  make  the  area  of  the  volute  at  its 
maximum  section  Fs  =  fz/n.1  The  value  of  n  may  be  determined 
from  equation  (55)  as 

_  Uz  —  v%  cos  02  _  4>  —  c  cos  a-2 

.  V2  C 

The  main  dimensions  which  affect  the  hydraulic  features  of  the 
pump  are  thus  determined.  The  question  may  be  raised  as  to 
what  assurance  we  have  that  the  maximum  efficiency  will  be 
attained  under  the  conditions  of  speed,  head,  and  discharge 
for  which  these  computations  were  made.  The  only  explanation 
is  that  the  values  of  0  and  c,  upon  which  the  computations  hinge, 
were  selected  according  to  values  obtained  with  previous  pumps 
for  their  points  of  maximum  efficiency.  Furthermore  all  dimen- 
sions and  angles  computed  were  determined  upon  the  supposition 
that  the  flow  specified  would  be  the  normal  flow  and  provisions 

1  If  the  velocity  throughout  the  case  is  uniform,  the  area  of  the  volute 
should  increase  directly  as  the  angle  measured  from  the  '  cutwater."  If 
the  cross-section  of  the  case  is  circular,  as  in  Fig-  9,  the  outer  boundary 
curve  is  a  parabolic  spiral  whose  equation  is  r  =  \/c0  +  K,  where  6  is  the 
angle  measured  from  the  "cutwater,"  K  is  the  radius  to  the  "cutwater," 
and  c  is  a  constant.  If  the  cross-section  of  the  case  is  rectangular,  the 
outer  boundary  curve  should  be  a  volute  the  diameter  of  whose  base  circle 
is  2K  sin  A,  where  K  has  the  same  meaning  as  in  the  former  instance, 
and  A  is  the  angle  with  the  tangent  made  by  the  stream  lines  entering 
the  case.  The  smaller  diameter  of  the  "nozzle"  will  be  TT  times  the 
diameter  of  the  base  circle.  The  actual  cross-sections  of  cases  are  rarely 
rectangular  and  often  not  even  circular. 


172 


CENTRIFUGAL  PUMPS 


were  made  to  minimize  all  the  losses  at  the  flow.  However  the 
actual  point  of  maximum  gross  efficiency  is  affected  by  the  me- 
chanical losses  as  well  as  the  hydraulic  losses.  It  might  be  neces- 
sary to  allow  for  this  if  it  were  not  for  the  fact  that  it  has  also  en- 
tered into  the  previous  pumps  for  which  our  values  of  <£  and  c 
were  experimentally  determined. 

126.  Layout  of  Impeller  Vanes. — The  theory  does  not  prescribe 
any  definite  curve  for  the  vanes  but  the  common  forms  are 
circular  arcs  and  involutes  or  rather  curves  with  involute  tips. 

To  lay  out  a  circular  arc  the  following  procedure  may  be 
employed:1  If  the  outer  and  inner  radii  are  OA  and  OB  respect- 


Circular  Arcs  (b)    With.ln volute  Tips 

FIG.  108. — Layout  of  impeller  vanes. 

ively  in  Fig.  108 (a),  lay  off  the  angle  OAC  =  az.  Lay  off  the 
angle  AOB  —  a2  +  «i-  Through  A  and  B  draw  the  line  intersect- 
ing the  circle  of  the  inner  diameter  at  E.  Erect  FG  as  a  perpendic- 
ular bisector  of  AE.  Through  G}  which  is  the  point  of  inter- 
section of  this  bisector  and  the  line  AC,  draw  a  circle  with  center 
at  0.  With  the  point  G  as  a  center  and  radius  GA  describe  the 
arc  AE.  This  is  the  vane  desired.  Other  centers  may  be  located 
on  the  circle  through  G  according  to  the  number  of  vanes.  The 
circular  arc  thus  constructed  will  be  found  to  make  the  required 
angles  a2  and  «i  at  exit  and  entrance  respectively. 

The  layout  of  vanes  with  involute  tips  is  shown  in  Fig.  108(6). 
With  0  as  a  center,  a  circle  may  be  described  whose  radius  OC 
=  OA  sin  a2,  where  OA  is  the  outer  radius  of  the  impeller.  Thus 

1  C.  G.  De  Laval,  "Centrifugal  Pumping  Machinery." 


DESIGN  OF  A  CENTRIFUGAL  PUMP  173 

the  angle  a2  is  the  angle  OAC.  With  this  circle  as  a  base  circle 
the  involute  AG  may  be  drawn.  The  involute  is  the  curve  traced 
by  the  point  A  as  the  imaginary  cord  CA  is  wound  around  a 
cylinder  of  which  the  base  circle  is  a  trace.  Thus  we  merely 
decrease  the  length  of  CA  by  the  length  of  the  arc  from  C  to  the 
point  of  tangency  of  the  line  on  which  we  are  to  lay  off  a  new 
radius.  If  the  involute  were  produced  until  it  reached  the  base 
circle,  the  angle  which  it  would  make  with  a  tangent  to  the  cir- 
cle at  that  point  would  be  90°.  It  is  impossible,  in  general,  to 
draw  a  complete  involute  for  the  entire  vane  as  the  angle  ai 
would  not  be  the  proper  value.  Therefore  only  AG  is  drawn  as 
an  involute. 

For  entrance  the  same  process  is  followed.  The  base  circle 
is  drawn  with  a  radius  OE  =  OF  sin  ai,  where  OF  is  the  inner 
radius  of  the  vanes.  With  this  base  circle  the  involute  FH  is 
drawn.  H  and  G  are  then  connected  by  a  smooth  curve.  It  is 
necessary  to  start  the  involute  at  the  proper  point  F  so  that  the 
two  tips  may  be  properly  joined  by  a  smooth  curve  HG.  This 
is  a  matter  of  trial,  but  can  be  easily  accomplished  by  drawing 
FH  on  a  piece  of  thin  paper  or  tracing  cloth  first. 

While  the  point  A  traces  one  involute  a  second  point  A'  may 
trace  a  second  involute  which  will  be  at  a  constant  distance  from 
the  first,  hence  the  two  curves  are  parallel.  Likewise  the  distance 
between  the  two  involutes  at  entrance  is  FFr  until  the  end  of  the 
second  involute  tip  is  reached. 

The  author  does  not  believe  that  one  form  of  vane  offers  any 
material  advantage  over  another  so  far  as  the  efficiency  of  the 
impeller  is  concerned.  The  involute  vanes  have  the  advantage 
that  it  is  easier  to  determine  the  angles  and  area  that  should  be 
used  in  the  formulas,  since  the  two  curves  are  parallel.  The  fact 
that  they  are  parallel  makes  it  more  reasonable  to  assume  that 
the  stream  lines  are  of  the  same  form  and,  therefore,  impellers 
with  involute  tips  are  more  amenable  to  mathematical  analysis. 

127.  Layout  of  a  Mixed  Flow  Impeller.— The  same  demands 
that  led  to  the  development  of  the  mixed  flow  reaction  turbine 
from  the  pure  radial  type  first  employed1  have  also  led  to  the  use 
of  the  mixed  flow  type  of  centrifugal  pump;  that  is  the  desire 
to  obtain  a  high  specific  speed. 

For  the  radial  flow  type  of  pump  the  impeller  vanes  may  be 
laid  out  as  in  Fig.  108,  since  the  curves  are  plane  curves.  But 

1  See  the  author's  "Hydraulic  Turbines,"  page  28. 


174 


CENTRIFUGAL  PUMPS 


with  the  mixed  flow  impeller  we  have  surfaces  of  double  curva- 
ture. It  should  be  noted  first  that  points  in  the  plan  view  of 
Fig.  109  are  actual  projections  of  the  points  upon  that  plane. 
But  the  elevation  view  shows  each  point  as  it  would  be  if  it  were 
rotated  about  the  axis  until  it  lay  in  the  plane  of  the  paper,  and 
does  not  show  actual  projections. 

The  procedure  is  as  follows:1  The  impeller  passage  is  divided 
up  into  parts  by  stream  lines  such  as  NN',  QQ',etc.,in  the  elevation 


M 


Horizontal  Plane 


FIG.  109. — Layout  of  a  mixed  flow  impeller. 

view.  The  ends  of  the  blades  such  as  NS  (in  the  elevation  view) 
are  regarded  as  lying  on  the  surface  of  a  cone  whose  vertex  is  at 
0.  For  Q  there  will  be  another  cone  whose  vertex  is  determined 
by  producing  the  stream  line  through  Q  until  it  intersects  the 
axis  of  rotation.  The  ends  of  the  blades  are  then  drawn  in  the 
customary  manner  but  upon  the  surfaces  of  these  developed 
cones,  such  as  that  at  the  right  for  the  point  N.  Since  u  varies 
with  r  it  will  be  necessary  for  a  to  also  vary  with  r  if  the  entrance 

1  This  is  an    abridgment  from  Loewenstein  and  Crissey,   "  Centrifugal 
Pumps,"  page  146. 


DESIGN  OF  A  CENTRIFUGAL  PUMP  175 

flow  is  to  be  radial  at  all  points.  We  should  thus  lay  out  a  dif- 
ferent curve  for  Q  from  the  one  for  N  as  well  as  have  it  on  the 
developed  surface  of  another  cone.  The  manner  of  transferring 
NS  from  the  developed  cone  to  the  two  views  is  readily  seen. 
The  location  for  N  in  the  plan  view  is  selected  at  will  and  then 
S  is  located  in  reference  to  it. 

In  the  plan  view  NSN'  is  drawn  as  a  smooth  curve  making  the 
required  angle  a2  at  N'.  To  determine  if  NSN'  in  the  plan  is  a 
proper  curve,  we  may  take  axial  sections  by  passing  planes 
parallel  to  the  axis,  and  containing  the  axis  if  the  entrance  arc 
is  in  a  radial  plane.  If  the  entrance  arc  is  not  in  a  radial  plane, 
these  axial  planes  should  be  parallel  to  the  plane  of  the  entrance 
arc.  Where  the  axial  plane  cuts  the  curve  in  the  plan  view,  such 
as  P,  it  is  possible  to  locate  a  corresponding  point  P  in  the  eleva- 
tion. A  number  of  such  points  for  this  one  axial  plane  and  other 
vane  curves  such  as  QQ',  etc.,  will  determine  a  line  APB.  This 
process  may  be  repeated  for  other  axial  planes  until  the  eleva- 
tion view  is  covered  with  curves  similar  to  APB.  If  proper  curves 
had  been  assumed  for  all  the  lines  such  as  NSN'  in  the  plan  view, 
APB  and  all  the  others  of  the  same  kind  in  the  elevation  would 
be  smooth  curves.  If  they  are  not  smooth,  the  curves  NSN',  etc., 
in  the  plan  should  be  altered,  but  always  in  such  a  way  that  they 
are  also  smooth. 

The  more  useful  curves  are  the  " pattern-maker's  curves'7 
which  are  obtained  with  horizontal  planes.  In  the  elevation  a 
single  horizontal  plane  is  shown  which  cuts  the  various  lines 
such  as  NSN'  at  P.  This  locates  P  on  the  curve  NSN'  in  the  plan 
view.  If  the  curve  MM'  were  drawn  in  the  plan  view,  the  point 
C  could  be  located  on  it  from  the  intersection  of  this  horizontal 
plane  with  MM'  in  the  elevation.  With  a  sufficient  number  of 
such  points  the  curve  CPN'  could  be  drawn.  This  is  the  actual 
curve  cut  by  the  one  horizontal  plane.  For  other  horizontal 
planes  similar  curves  could  be  obtained.  For  practical  use 
the  curves  would  be  obtained  for  planes  which  would  cover 
the  entire  height  of  the  impeller  blade  or  from  Mf  in  the  eleva- 
tion to  the  bottom  of  the  blade  below  R.  If  these  planes  are 
equidistant  from  each  other,  or  at  least  at  definite  distances 
apart,  the  curves  may  be  laid  out  on  boards  the  thicknesses  of 
which  are  exactly  equal  to  the  distances  between  planes.  After 
the  curves  are  sawed  out  the  boards  may  be  assembled  in 
the  proper  order  and,  after  smoothing  down,  the  exact  surface 


176 


CENTRIFUGAL  PUMPS 


of  a  blade  is  obtained.  In  order  to  properly  match  up  the 
boards  it  is  well  to  lay  out  each  curve  with  reference  to  a  right- 
angled  corner.  It  is  then  only  necessary  to  match  up  the 
corners  of  the  boards.  A  projection  of  a  set  of  pattern-maker's 
curves  is  shown  in  the  lower  right-hand  portion  of  Fig.  109. 
With  this  impeller  the  outlet  edge  M'R'  is  taken  as  being  parallel 
to  the  axis.  It  is  frequently  inclined,  in  which  event  M',  N', 
Q'}  R',  etc.,  would  not  coincide  in  the  plan  view. 


Section  B-E 

FIG.  110. — Centrifugal  pump  for  irrigation.     Capacity  =  31,500  G.P.M., 
h  =  59  ft.,  N  =  292  r.p.m.     (/.  P.  Morris  Co.) 


128.  Rating  Chart. — When  a  company  is  requested  to  supply 
a  centrifugal  pump  for  a  specified  speed,  head,  and  capacity, 
the  following  procedure  could  be  employed.  The  value  of 
the  specific  speed,  Na,  for  the  desired  pump  could  be  computed 
from  equation  (76).  It  would  then  be  known  at  once  whether 
any  one  of  their  standard  lines  of  pumps  would  be  suitable  for 
this  service.  If  they  did  build  a  pump  or  a  line  of  pumps 
having  approximately  this  same  value  of  the  specific  speed, 
that  type  would  fulfill  the  conditions.  To  determine  the  exact 
size  of  impeller  that  would  be  required,  equation  (72)  would 
be  employed,  using  the  value  of  KI  that  was  known  to  apply 
to  the  standard  line.  Since  pumps  are  rated  according  to 


DESIGN  OF  A  CENTRIFUGAL  PUMP 


177 


the  diameter  of  the  discharge  flange,  and  not  according  to  the 
impeller  diameter,  it  would  be  necessary  to  select  the  nominal 
pump  size.  This  could  be  done  either  by  having  an  established 
relation  between  the  diameter  of  the  discharge  flange  and  the 
diameter  and  width  of  the  impeller  or  by  using  a  certain 
definite  value  of  the  velocity  of  the  water  through  the  discharge 
flange.  Since  the  capacity  of  the  pump  is  given,  the  size  would 
be  directly  determined  by  the  latter  procedure.  (See  Art.  6.) 

The  selection  of  a  certain  pump  to  fulfill  these  conditions 
can  be  more  readily  accomplished  by  means  of  a  rating  chart, 
such  as  that  in  Fig.  111.1  This  diagram  may  be  laid  out  on 


316 
251 

1.200 
£» 

I       ^ 

&    100 

e 

79.5 


A 


x" 


x* 


Point  of  Max.  Efficiency 


T= 


23 


40     50     63    79.5   100    126    159    200   251    316    400    500    630    795  1000 
(Gallon  per  Minute)  /Vh 

FIG.  111. — Rating  diagram  for  centrifugal  pumps. 

logarithmic  cross-section  paper  or  on  regular  cross  section  paper. 
In  the  latter  event  logarithmic  scales  should  be  used.  The  data 
for  constructing  such  a  chart  should  be  determined  by  actual 
tests  of  various  sizes  of  pumps  so  as  to  secure  the  exact  head, 
speed,  and  capacity  at  which  the  maximum  efficiency  is  found. 

For  a  given  size  of  pump  (by  which  is  here  meant  the  diameter 
in  inches  of  the  discharge  flange)  a  point  of  maximum  efficiency 
can  be  located  for  values  of  N/^/h  and  G.P.M./\/h.  Three 
other  points  are  also  usually  located,  one  for  a  smaller  capacity 
at  90  per  cent,  of  the  maximum  efficiency,  and  two  for  larger 
capacities  at  95  and  90  per  cent,  of  the  maximum  efficiency. 
The  "type"  of  the  impeller,  that  is  the  ratio  D/B,  is  also  marked 
on  this  curve.  In  the  sample  chart  in  Fig.  Ill  only  two  "types" 
are  shown. 

Suppose  that  it  is  required  to  supply  a  pump  for  1,500  G.P.M. 
at  1,760  r.p.m.  under  a  head  of  125  ft.  per  stage.  The  value  of 

1  L.  J.  Bradford,  Eng.  News,  Vol.  72,  No.  8,  page  382. 

12 


178  CENTRIFUGAL  PUMPS 


is  157  and  that  of  G.P.M./^/h  is  135.  This  point  is 
shown  on  the  chart.  If  this  point  fell  on  one  of  the  curves, 
the  pump  for  which  that  curve  was  constructed  would  be  the  one 
required.  If  the  maximum  efficiency  does  not  occur  here,  it 
simply  means  that  the  head  and  capacity  of  the  pump  is  a 
trifle  different  from  the  values  specified.  The  efficiency  under 
the  exact  conditions  specified  would  be  a  certain  per  cent,  of  the 
maximum  efficiency,  which  could  be  estimated.  In  the  figure 
Shown,  this  point  does  not  fall  on  one  of  the  curves,  though  it 
might  do  so,  if  other  "  types"  had  also  been  plotted.  But 
suppose  these  two  lines  of  pumps  are  all  that  are  available.  It 
is  seen  that  an  8-in.  pump  of  type  23  is  a  trifle  too  large  for  the 
conditions.  It  cpuld  be  made  to  fit  the  case  by  cutting  the  vanes 
back  a  little,  as  this  would  reduce  the  effective  diameter  of  the 
impeller.  Under  the  conditions  shown,  it  is  seen  that  the  pump 
would  operate  at  about  98  per  cent,  of  its  maximum  efficiency. 

This  chart  is  constructed  for  single-stage  pumps  only.  It 
would  be  possible  to  add  other  curves  similar  to  these  but  on 
other  parts  of  the  field  for  various  numbers  of  stages. 

129.  PROBLEMS 

1.  Design  a  centrifugal  pump  to  deliver  900  G.P.M.  at  a  head  of  40  ft. 
when  running  at  2,000  r.p.m.     (The  data  for  the  pumps  described  in  Art.  53 
will  serve  as  guides  in  this.) 

2.  Construct  the  curve  for  the  Worthington  pump  of  Art.  53  in  the  rating 
chart,  Fig.  111. 

3.  Using  the  rating  chart  of  Fig.  Ill,  select  the  size  of  pump  to  deliver 
4,000  G.P.M.  at  a  head  of  100  ft.  when  running  at  1,000  r.p.m.     If  the 
maximum  efficiency  of  the  pump  selected  is  72  per  cent.,  what  will  its  effi- 
ciency probably  be  under  the  required  conditions  ?     What  would  the  capacity 
have  to  be  under  this  head  and  speed  for  the  maximum  efficiency  of  this 
pump  to  be  attained? 


APPENDIX  A 


TEST  DATA 

The  test  data  of  the  pumps  for  which  the  characteristics  in 
Chapter  VI  were  plotted  will  be  found  in  Tables  1  and  2.  This 
data  is  from  careful  tests  performed  by  the  author  with  the  assist- 
ance of  F.  G.  Switzer  upon  two  centrifugal  pumps  in  the  hy- 
draulic laboratory  of  Sibley  College.  The  water  was  measured 
by  weirs,  which  had  been  thoroughly  calibrated  with  the  aid  of 
a  large  weighing  tank.  Pressures  were  read  by  mercury  ma- 
nometers or  by  pressure  gages  of  suitable  scales  which  were  cali- 
brated by  comparison  with  a  dead  weight  gage  tester.  The 
pumps  were  driven  by  electric  motors,  the  losses  of  which  were 
determined,  so  that  the  brake  horse-power  could  be  computed 
from  the  electrical  readings. 

The  test  data  in  Tables  3  and  4  was  supplied  by  the  Platt 
Iron  Works  Co. 

TABLE  1. — TEST  OP  A  2.5-iN.  TWO-STAGE  WORTHINGTON  TURBINE  PUMP 
(By  R.  L.  Daugherty) 


Run 

R.p.m. 

Discharge, 
cu.  ft.  per  sec. 

Total  head, 
ft. 

B.h.p. 

Efficiency, 
per  cent. 

1 

700 

0.000 

43.6 

0.705 

00.0 

2 

700 

0.028 

40.5 

0.788 

16.4 

3 

700 

0.067 

44.7 

0.990 

34.3 

4 

700 

0.100 

44.8 

1.190 

42.7 

5 

700 

0.108 

44.8 

1.246 

44.0 

6 

700 

0.148 

42.3 

1.490 

47.9 

7 

700 

0.230 

30.3 

1.760 

45.2 

8 

700 

0.295 

13.1 

1.950 

22.5 

9 

,000 

0.000 

85.1 

2.06 

00.0 

10 

,000 

0.062 

86.2 

2.60 

23.5 

11 

,000 

0.110 

92.2 

3.00 

38.3 

12 

,000 

0.150 

91.2 

3.39 

45.9 

13 

,000 

0.196 

86.2 

3.92 

49.0 

14 

,000 

0.233 

80.1 

4.27 

49.7 

15 

,000 

0.308 

66.3 

4.83 

48.0 

16 

,000 

0.343 

59.7 

5.28 

44.0 

17 

,000 

0.408 

35.8 

5.57 

29.8 

18 

,000 

0.436 

15.5 

5.53 

14.2 

179 


180  CENTRIFUGAL  PUMPS 

TABLE    1. — TEST 'OF  A  2.5-iN.  TWO-STAGE  WORTHINGTON  TURBINE  PUMP 
(By  R.  L.  Daugherty). — Continued 


Run 

R.p.m. 

Discharge, 
cu.  ft.  per  sec. 

Total  head, 
ft. 

B.h.p. 

Efficiency, 
per  cent. 

19 

1,200 

0.000 

124.1 

3.38 

00.0 

20 

1,200 

0.060 

124.2 

4.11 

20.6 

21 

1,200 

0.117 

127.7 

4.65 

36.6 

22 

1,200 

0.167 

130.9 

5.43 

45.7 

23 

1,200 

0.215 

126.7 

6.22 

49.7 

24 

1,200 

0.283 

115.2 

7.22 

51.4 

25 

1,200 

0.348 

99.5 

7.85 

50.2 

26 

1,200 

0.390 

84.8 

8.15 

46.2 

27 

1,200 

0.450 

64.0 

8.78 

37.2 

28 

1,200 

0.494 

20.3 

8.87 

12.9 

29 

1,400 

0.000 

172.8 

5.41 

00.0 

30 

1,400 

0.097 

173.1 

6.88 

28.6 

31 

1,400 

0.198 

180.5 

8.90 

45.6 

32 

1,400 

0.302 

176.5 

10.85 

55.8 

33 

1,400 

0.373 

146.8 

11.95 

52.2 

34 

1,400     . 

0.412 

140.1 

12.64 

51.7 

35 

,400 

0.455 

115.5 

13.27 

45.1 

36 

,400 

0.518 

67.3 

13.50 

29.4 

37 

,400 

0.541 

23.3 

13.40 

10.7 

38 

,600 

0.000 

226.8 

8.18 

00.0 

39 

,600 

0.112 

227.2 

10.44 

27.8 

40 

,600 

0.226 

235.3 

12.95 

46.7 

41 

,600 

0.310 

228.5 

15.22 

52.8 

42 

,600 

0.415 

200.5 

17.51 

54.0 

43 

,600 

0.470 

175.1 

18.60 

50.2 

44 

1,600 

0.512 

139.4 

18.08 

45.0 

45 

1,600 

0.550 

72.2 

18.15 

24.9 

46 

1,600 

0.565 

25.2 

17.35 

09.3 

47 

1,700 

0.000 

248.5 

9.13 

00.0 

48 

1,700 

0.049 

248.6 

10.12 

13.7 

49 

1,700 

0.112 

254.7 

11.78 

27.6 

50 

1,700 

0.155 

257.5 

12.70 

35.8 

51 

1,700 

0.236 

264.1 

15.08 

47.1 

52 

1,700 

0.348 

248.8 

18.15 

54.3 

53 

1,700 

0.429 

225.0 

20.06 

55.0 

54 

1,700 

0.494 

192.3  , 

21.60 

50.0 

55 

1,700 

0.531 

157.3 

22.00 

43.2 

56 

1,700 

0.573 

73.1 

21.25 

22.4 

57 

1,700 

0.578 

47.0 

20.60 

15.0 

58 

1,700 

0.580 

26.3 

20.15 

08.6 

59 

1,800 

0.000 

280.8 

10.58 

00.0 

APPENDIX  A 


181 


TABLE  1. — TEST  OF  A  2.5-iN.  TWO-STAGE  WORTHINGTON  TURBINE  PUMP 
(By  R.  L.  Daugherty). — Continued 


Run 

R.p.m. 

(Discharge, 
cu.  ft.  per  sec. 

Total  head, 
ft. 

B.h.p. 

Efficiency, 
per  cent. 

60 

1,800 

0.137 

281.3 

14  '.43 

30.4 

61 

1,800 

0.221 

297.2 

16.70 

44.7 

62 

1,800 

0.293 

292.1 

19.38 

50.2 

63 

1,800 

0.403 

268.4 

22.65 

54.3 

64 

1,800 

0.510 

221.2 

24.80 

51.8 

65 

1,800 

0.568 

140.9 

24.60 

36.9 

66 

1,800 

0.580 

90.0 

23.90 

24.8 

67 

1,800 

0.584 

51.4 

23.00 

14.8 

68 

1,800 

0.585 

22.0 

22.90 

07.8 

69 

2,000 

0.000 

346.8 

15.00 

00.0 

70 

2,000 

0.105 

349.4 

18.20 

22.9 

71 

2,000 

0.247 

368.1 

23.00 

44.8 

72 

2,000 

0.327 

362.6 

26.30 

51.2 

73 

2,000 

0.590 

27.4 

28.30 

06.5 

74 

708 

0.31 

75 

964 

0.62 

76 

1,132 

0.69 

77 

1,344 

Pump  free  f 

rom  water 

0.84 

78 

1,512 

0.99 

79 

1,846 

1.76 



TABLE  2. — TEST  OF  A  6-iN.   SINGLE-STAGE   DOUBLE-SECTION  DE  LAVAL 

VOLUTE  CENTRIFUGAL  PUMP 
(At  a  Constant  Speed  of  1,700  r.p.m.) 


Run 

Discharge, 
cu.  ft,  per  sec. 

Total  head,  ft. 

B.h.p. 

Efficiency, 
per  cent. 

1 

0.000 

68.5 

4.3 

00.0 

2 

0.068 

68.4 

4.5 

11.8 

3 

0.188 

69.6 

5.2 

28.6 

4 

0.320 

69.3 

6.0 

42.0 

5 

0.606 

69.2 

7.8 

61.1 

6 

0.840 

66.7 

9.4 

67.7 

7 

0.933 

65.5 

9.7 

71.6 

8 

1.063 

62.7 

10.3 

73.3 

9 

1.315 

55.7 

11.3 

73.7 

10 

1.632 

47.3 

12.0 

73.3 

11 

1.968 

35.7 

11.8 

67.7 

12 

2.090 

28.1 

11.5 

58.0 

13 

2.240 

22.3 

11.2 

50.7 

182 


CENTRIFUGAL  PUMPS 


TABLE  3. — TEST    OF    AN    18-iN.    SINGLE-STAGE    DOUBLE  SUCTION  PLATT 

CENTRIFUGAL  PUMP 
(Volute  Type.     Impeller  Diameter  =  15.5  in.) 


R.p.m. 

G.P.M. 

Head,  ft. 

B.h.p. 

Efficiency, 
per  cent. 

1,135 

7,700 

24.0 

94.5 

50.0 

1,140 

7,670 

33.0 

107.0 

60.0 

1,140 

7,610 

41.0 

111.0 

71.0 

1,135 

7,320 

49.5 

120.0 

76.5 

1,140 

6,700 

59.5 

124.0 

81.0 

1,140 

5,950 

66.5 

124.0 

80.5 

1,140 

5,050 

72.5 

120.0 

77.5 

1,135 

3,775 

77.5 

110.0 

67.5 

1,140 

3,260 

78.0 

100.0 

64.2 

1,140 

2,550 

79.0 

91.0 

56.0 

1,145 

0 

80.0 

57.5 

00.0 

TABLE  4. — TEST  OF  A  26-iN.  SINGLE-STAGE  DOUBLE  SUCTION  PLATT 

CENTRIFUGAL  PUMP 

(Volute  Type) 


R.p.m. 

G.P.M. 

Head,  ft. 

B.h.p. 

Efficiency, 
per  cent. 

465 

16,460 

25.8 

127.5 

84.0 

465 

16,780 

26.0 

127.5 

86.0 

465 

15,850 

26.8 

127.0 

84.5 

465 

14,850 

27.9 

124.0 

84.0 

470 

13,750 

29.1 

123.0 

82.0 

472 

12,400 

32.5 

122.5 

81.0 

480 

9,220 

36.0 

117.5 

71.0 

550 

0 

48.0 

101.5 

00.0 

450 

0 

30.0 

45.0 

0.00 

APPENDIX  B 

REVIEW  QUESTIONS 

1.  What  is  a  centrifugal  pump?     Why  is  it  so  called? 

2.  How  are  centrifugal  pumps  classified? 

3.  What  is  a  whirlpool  chamber? 

4.  What  is  a  rising  characteristic? 

5.  What  is  a  flat  characteristic? 

6.  What  is  a  steep  characteristic? 

7.  Why  is  the  modern  centrifugal  pump  a  recent  development? 

8.  To  what  heights  may  water  be  lifted  by  centrifugal  pumps? 

9.  How  large  may  be  the  capacities  of  centrifugal  pumps? 

10.  What  rotative  speeds  are  commonly  found? 

11.  How  many  stages  may  be  employed  with  centrifugal  pumps? 

12.  What  is  the  usual  range  of  head  per  stage? 

13.  What  "size"  of  centrifugal  pump  would  be  required  to  discharge 
900G.P.M.? 

14.  What  is  meant  by  "normal  discharge?" 

15.  What  types  of  impellers  are  there? 

16.  How  are  impellers  constructed? 

17.  What  is  meant  by  the  "type"  of  an  impeller? 

18.  What  is  the  function  of  the  diffuser? 

19.  How  is  velocity  converted  into  pressure  in  a  volute  pump? 

20.  What  are  labyrinth  rings? 

21.  How  is  air  prevented  from  leaking  in  around  the  shaft  at  the  suction 
end? 

22.  What  types  of  cases  are  there?     What  are  their  relative  merits? 

23.  What  is  the  Jaeger  type  of  pump?     The  Kugel-Gelpe  type?     The 
Sulzer  type? 

24.  What  are  the  relative  merits  of  the  four  types  of  pumps  (adding  the 
Rateau  to  the  above  named)  ? 

25.  What  causes  end  thrust? 

26.  What  is  hydraulic  balancing? 

27.  What  are  balancing  pistons?     How  do  they  operate? 

28.  How  are  pumps  primed? 

29.  Of  what  use  are  foot  valves? 

30.  Of  what  use  is  a  check  valve  on  the  discharge  side? 

31.  Of  what  use  is  a  gate  valve  on  the  discharge  side? 

32.  What  limits  the  allowable  suction  lift? 

33.  What  is  the  effect  of  slight  air  leakage  in  the  suction  pipe  upon  the 
operation  of  the  pump  ? 

34.  What  is  the  effect  of  the  liberation  of  air  that  may  be  in  solution  in  the 
water  in  the  suction  pipe? 

183 


184  CENTRIFUGAL  PUMPS 

36.  What  is  the  effect  of  the  formation  of  water  vapor  due  to  too  low  a 
pressure  in  the  suction  pipe? 

36.  What  kind  of  piping  connections  are  desirable?     Why? 

37.  What  will  be  the  effect  of  placing  two  pumps  in  series?     In  parallel? 
How  does  this  affect  the  efficiency?     Why? 

38.  What  procedure  would  you  follow  in  starting  up  a  centrifugal  pump? 

39.  Given  u  =  50  ft.  per  sec.,  V  =  40  ft.  per  sec.,  A  =  20°,  find  v  and  a. 

40.  Given  V  =  100  ft.  per  sec.,  A  =  30°,  what  is  the  value  of  s? 

41.  If  u  =  60  ft.  per  sec.,  v  =  20  ft.  per  sec.,  what  is  the  value  of  s  if 
a  =  20°?     (b)  If  a  =  90°?     (c)  If  a  =  120°? 

42.  In  what  ways  may  the  area  of  the  impeller  passages  be  computed? 
Do  these  two  methods  give  identical  results? 

43.  What  is  "head?"     What  is  its  energy  meaning? 

44.  How  would  the  head  against  which  a  pump  must  work  be  computed 
from  the  pipe  line  specifications? 

45.  How  would  the  head  against  which  a  pump  works  be  computed  from 
data  taken  at  the  pump? 

46.  What  is  the  distinction  between  a  forced  vortex  and  a  free  vortex? 

47.  What  is  the  difference  between  the  variation  of  the  pressure  with  the 
radius  of  rotation  in  the  cases  of  a  free  and  a  forced  vortex? 

48.  What  is  "brake  horse-power?"     Why  is  it  so  called? 

49.  What  is  water  horse-power? 

50.  What  is  the  physical  meaning  of  the  "power  .imparted  to  the  water 
by  the  impeller?" 

51.  What  is  gross  efficiency?     Mechanical  efficiency?     Volumetric  effi- 
ciency?    Hydraulic  efficiency? 

52.  What  is  meant  by  duty? 

53.  What  are  the  advantages  of  guide  vanes  at  entrance  to  a  centrifugal 
pump  impeller? 

54.  What  is  the  difference  between  h"  and  /i? 

55.  What  is  the  difference  between  hydraulic  efficiency  and  manometric 
coefficient? 

56.  Why  does  not  the  maximum  hydraulic  efficiency  occur  when  the 
shock  loss  is  zero? 

57.  Why  does  not  the  maximum  gross-efficiency  occur  where  the  hydraulic 
efficiency  is  a  maximum? 

58.  What  effect  has  the  number  of  vanes  upon  the  characteristics  of  an 
impeller? 

59.  What  are  the  defects  inherent  in  the  ordinary  hydraulic  theory? 

60.  Is  the  vane  angle  necessarily  the  value  that  should  be  used  for  a2 
in  the  theoretical  equations? 

61.  Is  the  area  of  the  impeller  passages  the  actual  effective  area  of  the 
streams? 

62.  What  can  be  done  to  overcome  the  defects  of  the  theory? 

63.  Of  what  value  may  a  theory  be  that  does  not  yield  numerically  exact 
answers? 

64.  What  considerations  affect  the  selection  of  a  value  for  #2?     For  A '2? 

65.  If  the  dimensions  of  a  pump  are  given,  what  equations  would  you  use 
to  find  by  theory  the  values  of  0  and  c  for  the  maximum  hydraulic  efficiency? 


APPENDIX  B  185 

66.  What  equations  would  you  use  to  find  the  values  of  0  and  cfor which 
the  shock  loss  in  the  turbine  pump  is  zero? 

67.  Given  all  the  essential  dimensions  and  a  specified  value  of  <f>  (not 
necessarily  the  best),  what  equations  would  you  use  to  find  the  hydrauli6 
efficiency  by  theory? 

68.  What  causes  a  point  of  inflection  in  the  head-discharge  curves  of  some 
pumps  at  constant  speed  for  small  values  of  the  rate  of  discharge? 

69.  Why  is  it  desirable  that  the  b.h.p.  curve  for  a  pump  at  constant  speed 
reach  its  maximum  before  the  maximum  value  of  the  rate  of  discharge  is 
attained? 

70.  The  water  horse-power  of  a  pump  at  maximum  efficiency  varies  as 
what  power  of  the  speed?     ^ 

71.  Why  does  not  the  b.h.p.  of  a  pump  at  maximum  efficiency  vary  as 
the  cube  of  the  speed?     When  will  the  power  be  less  than  the  cube?     When 
higher? 

72.  Is  there  any  limit  to  the  capacity  of  a  given  centrifugal  pump  if  its 
speed  be  indefinitely  increased? 

73.  What  practical  cases  might  be  found  where  a  pump  was  required  to 
deliver  approximately  a  constant  rate  of  discharge  under  a  varying  head? 
How  can  this  be  accomplished  with  a  centrifugal  pump?     Which  way  is 
most  economical? 

74.  For  an  ordinary  pipe  line  with  friction  what  is  the  most  efficient 
way  to  operate  a  centrifugal  pump  for  a  varying  rate  of  discharge?     Which 
way  is  simpler  and'  cheaper  in  first  cost? 

75.  What  is  meant  by  efficiency  of  a  pipe  line? 

76.  Why  may  a  pipe  300  ft.  long  elevating  water  a  height  of  200  ft.  have 
a  higher  efficiency  than  another  one  3,000  ft.  long  delivering  water  at  a  height 
of  50  ft?     Would  it  be  a  physical  possibility  for  them  to  have  the  same 
efficiency? 

77.  Assuming  the  friction  factor  to  be  0.03  for  all  cases  and  neglecting 
minor  losses,  what  would  be  the  diameter  of  pipe  necessary  for  an  efficiency 
of  90  per  cent,  in  each  case  in  (76)?     For  an  efficiency  of  60  per  cent.? 

78.  Which  gives  the  greater  amount  of  disk  friction  for  a  given  peripheral 
velocity,  a  small  diameter  of  impeller  at  a  high  rotative  speed  or  a  large 
diameter  of  impeller  at  a  low  rotative  speed? 

79.  Is  the  shrouded  type  of  impeller  more  desirable  than  the  open  type 
so  far  as  disk  friction  is  concerned? 

80.  To  reduce  the  disk  friction  of  an  impeller  is  it  desirable  to  have  the 
clearance  large  or  small? 

81.  Should  the  interior  of  the  pump  case  be  smooth?     Why? 

82.  Will  the  test  of  a  centrifugal  pump  at  a  certain  speed  determine  the 
efficiency  for  another  speed? 

83.  Why  is  the  efficiency  of  a  large  capacity  pump  higher  than  that  of  a 
small  capacity  pump? 

84.  How  may  a  high  specific  speed  be  attained  in  the  construction  of  a 
centrifugal  pump? 

85.  Of  what  advantage  may  a  high  specific  speed  be? 

86.  What  determines  the  number  of  stages  into  which  a  pump  is  to  be 
divided? 


186  CENTRIFUGAL  PUMPS 

87.  What  are  the  natures  of  the  characteristics  of  the  displacement 
pump?     How  do  they  compare  with  those  of  the  centrifugal  pump? 

88.  What  are  the  relative  merits  of  displacement  and  centrifugal  pumps? 

89.  What  seems  to  be  the  difference  in  the  efficiencies  of  turbine  and 
volute  pumps? 

90.  Is  there  any  difference  between  the  efficiencies  of  pumps  with  rising 
and  falling  characteristics? 

91.  When  would  a  turbine  pump  be  preferable  to  a  volute  pump?     When 
would  the  volute  pump  be  preferable? 

92.  When  is  a  pump  with  a  steep  characteristic  desirable? 

93.  What  uses  may  be  made  of  the  specific  speed  factor? 

94.  For  a  given  total  head  and  capacity,  how  does  the  value  of  the  specific 
speed  change  as  the  number  of  stages  is  varied? 

96.  For  what  purposes  would  a  pump  be  tested? 

96.  What  precautions  should  be  observed  in  attaching  a  gage  to  a  pipe 
for  the  measurement  of  pressure? 

97.  Why  should  the  connections  between  the  pipe  and  the  gage  be  filled 
with  water? 

98.  Why  should  the  difference  between  the  velocity  heads  at  suction  and 
discharge  be  considered  in  computing  the  head  developed  by  a  pump? 

99.  How  should  a  weir  formula  be  chosen? 

100.  For  a  uniform  rate  of  pumping,  which  type  of  pump  may  be  more 
economical,  the  centrifugal  or  the  reciprocating? 

101.  For  intermittent  service,  which  type  is  more  economical,  the  cen- 
trifugal or  the  reciprocating? 

102.  Which  type  of  pumping  unit,  centrifugal  or  reciprocating,  is  apt  to 
be  better  where  fuel  is  cheap? 

103.  What  are  the  advantages  of  a  screw  pump? 

104.  What  conditions  are  favorable  to  the  use  of  a  centrifugal  pumping 
unit? 

105.  What  conditions  are  favorable  to  the  use  of  a  reciprocating  pump- 
ing unit? 


APPENDIX   C 


TABLE  OF  THE  %  POWERS  OF  NUMBERS  FROM  1  TO  300 
(For  Example  16%.  =8.00) 


0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

0 

0.00 

1.00 

1.68 

2.28 

2.83 

3.34 

3.83 

4.30 

4.75 

5.20 

1 

5.62 

6.03 

6.45 

6.85 

7.24 

7.62 

8.00 

8.38 

8.73 

9.09 

2 

9.45 

9.80 

10.15 

10.50 

10.83 

11.18 

11.50 

11.85 

12.18 

12.50 

3 

12.8213.14 

13.45 

13.78 

14.10 

14.38 

14.70 

15.01 

15.30 

15.63 

4 

15.90 

16.20 

16.50 

16.80 

17.08 

17.38 

17.65 

17.95 

18.25 

18.54 

5 

18.80 

19.19 

19.38 

19.64 

19.91 

20.20 

20.45 

20.75 

21.00 

21.30 

6 

21.65 

21.80 

22.10 

22.36 

22.62 

22.90 

23.17 

23.42 

23.70 

23.92 

7 

24.20 

24.45 

24.71 

25.00 

25.24 

25.47 

25.75 

26.00 

26.22 

26.47 

8 

26.77 

27.00 

27.25 

27.50 

27.75 

27.98 

28.23 

28.50 

28.74 

28.99 

9 

29.23 

29.45 

29.70 

29.98 

30.20 

30.44 

30.67 

30.90 

31.13 

31.40 

10 

31.6 

31.9 

32.1 

32.3 

32.6 

32.8 

33.0 

33.2 

33.5 

33.7 

11 

33.9 

34.2 

34.4 

34.6 

34.8 

35.0 

35.3 

35.5 

35.8 

36.0 

12 

36.2 

36.5 

36.7 

36.9 

37.1 

37.4 

37.6 

37.8 

38.1 

38.3 

13 

38.5 

38.7 

39.0 

39.2 

39.4 

39.6 

39.8 

40.0 

40.2 

40.4 

14 

40.6 

40.8 

41.0 

41.3 

41.6 

41.8 

42.0 

42.2 

42.4 

42.6 

15 

42.8 

43.0 

43.2 

43.5 

43.7 

43.9 

44.1 

44.4 

44.6 

4'4.8 

16 

45.0 

45.2 

45.4 

45.7 

45.8 

46.0 

46.2 

46.4 

46.7 

46.9 

17 

47.1 

47.2 

47.4 

47.7 

47.9 

48.1 

48.3 

48.5 

48.7 

49.0 

18 

49.2 

49.3 

49.5 

49.7 

49.9 

50.2 

50.4 

50.6 

50.8 

51.0 

19 

51.2 

51.4 

51.6 

51.8 

52.0 

52.2 

52.4 

52.6 

52.8 

53.0 

20 

53.2 

53.4 

53.6 

53.8 

54.0 

54.2 

54.4 

54.6 

54.7 

54.9 

21 

55.1 

55.3 

55.6 

55.8 

56.0 

56.2 

56.4 

56.6 

56.7 

56.9 

22 

57.1 

57.3 

57.5 

57.7 

57.9 

58.1 

58.3 

58.5 

58.6 

58.8 

23 

59.0 

59.3 

59.5 

59.6 

59.8 

60.0 

60.2 

60.4 

60.5 

60.8 

24 

61.0 

61.2 

61.4 

61.6 

61.8 

62.0 

62.1 

62.4 

62.5 

62.7 

25 

62.9 

63.1 

63.3 

63.4 

63.6 

63.8 

64.0 

64.2 

64.4 

64.6 

26 

64.8 

65.0 

65.2 

65.4 

65.6 

65.8 

66.0 

66.1 

66.2 

66.4 

27 

66.6 

66.8 

67.0 

67.2 

67.4 

67.6 

67.7 

67.9 

68.0 

68.2 

28 

68.4 

68.6 

68.8 

69.0 

69.2 

69.4 

69.6 

69.8 

70.0 

70.1 

29 

QH 

70.2 

70  0 

70.4 

70.6 

70.8 

71.0 

71.2 

71.4 

71.5 

71.6 

71.8 

O\J 

4  4  .  \J 

187 


INDEX 


Abbreviations,  56 

Absolute  path  of  water,  2,  60 

velocity,  45 
Air  in  suction,  41 
Analysis  of  centrifugal  pumps,  75 
Angles  0,2  and  A'?,  85 
Angular  momentum,  59 
Annual 'cost  of  pumping,  155 
Appold,  10 

Average  efficiency,  133 
Axial  thrust,  see  Thrust. 

B 

Balancing,  30 

pistons,  36 
Blade,  see  Vane. 
Boiler  feed  pumps,  161 
Brake  horse-power,  54 

C 

Calculation  of  impeller,  170 

Capacities,  11 

Capacity,  effect  on  efficiency,  114 

factor,  138 
Capital  cost,  155 
Cases,  23 

form  of,  171 
Cavitation,  92 
Centrifugal  action,  50 

head,  69 

Centrifugal  pump,  action  of,  1 
•     advantages  of,  130 

crude,  52 

definition  of,  1,  6 
Characteristic,  classification  as  to, 

curves  or  diagram,  104 

definition,  88 

rising  vs.  falling,  134 
Churning  loss,  76 


Circular  arc  vanes,  172 

Classification,  1 

Clearance  rings,  22 

Condenser  circulating  pumps,  160 

Conditions  of  use,  11 

Construction  of  vane  curves,  172 

Continuity,  equation  of,  46 

Conversion  factors,  56 

Cost  of  cheap  stock  pumps,  153 

pumping,  155 
Curved  vanes,  introduction  of,  10 


Defects  of  theory,  79 
De  Laval  pump,  dimensions  of,  89 
Design  of  impeller,  169 
Development  of  centrifugal  pump,  9 
Diameter  of  impeller  and  capacity, 

139 
Diffusion  vanes,  advantages  of,  68 

angle  of,  85 

description  of,  21 

introduction  of,  10 

use  of,  1 
Directing  vanes,  see  Diffusion  vanes, 

see  Guide  vanes. 
Discharge,  diagram,  66 

losses  of  impeller,  66 

losses  of  pipe,  49 

measurement  of,  139 
Disk  friction,  107 

approximate  formulas  for,  109 

experimental  results,  108 
Displacement  pumps,  advantages  of, 
130 

characteristics  of,  129 

comparison  with,  128 
Drag  of  impeller,  see  Disk  friction. 
Double  suction,  16 
Dredging  pumps,  165 
Duty,  55 


189 


190 


INDEX 


K 


Efficiency,  definition  of,  54 

as  a  function  of  capacity,  114 
of  head,  117 

of  number  of  stages,  124 
of  specific  speed,  120 

factors  affecting,  125 

vs.  discharge  curves,  95 

hydraulic,  55,  73 

maximum,  97 

mechanical,  54 

of  pump  and  pipe  line,  103 

of  pumping,  102 

of  a  series  of  pumps,  112 

of  a  single  pump,  111 

total,  55 

volumetric,  55 
Empirical  design,  168 

modification  of  theory,  82 
Enclosed  impeller,  16 
End  thrust,  30 
Energy,  equation  of,  47 
Entrance  diagram,  65 

losses  in  pipe,  49 
Euler,  9 

Exit  losses  of  impeller,  66 
Experimental  analysis,  75 
Eye  of  impeller,  2 


Factors,  72,  136 
Falling  characteristic,  7,  63 
Fire  pumps,  161 
Fixed  charges,  155 
Flat  characteristic,  7,  63 
Foot  valve,  40 
Friction  in  pipe,  48 
losses  in  pump,  64 

G 

Gland  cage,  22 

Gross  efficiency,  see  Total  efficiency. 

Guide  vanes  at  exit,  see  Diffusion 

vanes   in   eye,    advantages 

of,  62 


H 


Head,  computed  by  theory,  71 
developed  by  pump,  49 
discharge  curves,  89 
effect  on  efficiency  of,  117' 
imparted  by  impeller,  62 
of  impending  delivery,  69 
losses  in  pipe,  48 
losses  in  pump,  54,  64 
meaning  of,  47 
shut-off,  69 
Heads  of  pumps,  11 
Helicoidal  impeller,  123 
Historical  development,  9 
Horse-power,  largest,  13 
Hydraulic  balancing,  36 
efficiency,  55 


Impeller,  16 

helicoidal,  123 
Impending  delivery,  69,  96 
Imperfections  of  theory,  79 
Involute  vanes,  construction  of,  172 
Iso-efficiency  curves,  104 


Jaeger  type,  25 
Jordan,  9 


K 


Kugel-Gelpe  type,  25 
L 

Labyrinth  rings,  22 
Leakage  of  air,  effect  of,  41 

losses,  30,  54,  78 
Lift,  see  Head. 
Losses  of  head  in  pipes,  48 

pumps,  54,  64 

M 

McCarty  pump,  10 
Manometric  coefficient,  73 
values  of,  169 


INDEX 


191 


Massachusetts  pump,  10 
Maximum  efficiency,  conditions  for, 
125 

of  turbine  vs.  volute  pumps,  132 
Measurement  of  head,  146 

speed,  150 

water,  147 
Mechanical  efficiency,  54 

losses,  54,  111 
Mine  pumps,  164 
Mixed  flow  impeller,  173 
Multi-impeller,  124 
Multi-stage,  introduction  of,  10 

meaning  of,  7 

N 

Normal  discharge,  15 
Notation,  44 
Nozzle,  3 

Number  of  pump,  15 
of  vanes,  79 


Open  impeller,  16 
Operating  expenses,  155 
Operating  a  pump,  43 
Opposed  impellers,  35 


Packing,  22 

Papin,  9 

Parallel  operation,  42 

Pattern  maker's  curves,  175 

Pipe  efficiency,  103 

friction,  48 
Pitot  tube,  148 
Plotting  curves,  151 
Power-discharge  curves,  94 

measurement  of,  151 
Pressure,  negative,  1 

positive,  1 

transformation,  2,  53 
Priming,  40 
Propeller  pump,  159 
Pulsation  of  flow,  42 


H 


Rateau,  32 

Rated  capacity,  15 
discharge,  15 
head,  15 

Rating  chart,  176 

Reaction  turbine,  comparison  with, 
8 

Reciprocating  pump,  comparative 
cost  of,  129,  see  Displace- 
ment pump. 

Reduction  gears,  166 

Relative  velocity,  45 

Reversing  channels,  25 

Rings,  clearance,  22 

Rising  characteristic,  7,  63 

Rotary  pump,  158 


Screw  pump,  159 

Scroll  case,  22 

Sectional  cases,  24 

Series  operation,  42 

Series  of  pumps,  efficiency  of,  112 

Shock  loss,  65 

Short  circuited  water,  30,  54,  78 

Shroud,  16 

Shut-off  head,  69,  96 

Side  plate  type,  7 

merits  of,  23 
Side  suction,  16 
Single  suction,  16 

stage,  7 

Size  of  pump,  15 
Solid  case,  24 
Specific  speed,  derivation  of,  139 

efficiency  a  function  of,  120 
high  values  of,  122 

values  of,  141 
Speeds,  14 

effect  on  efficiency,  118 

measurement  of,  150 
Split  case,  7 

advantages  of,  23 
Stages,  number  of,  14 

effect  of  number  of,  124 
Static  head,  50 


192 


INDEX 


Steam  power  plant,  pumps  for,  160 

turbine  driven  centrifugal,   12, 

123,  165 

Steep  characteristic,  7 
Strainers,  40 
Stuffing  boxes,  22 
Suction,  double,  16 

gland,  22 

lift,  41 

rotation  in,  61 

side  or  single,  16 


Tachometer,  150 
Test  data,  179 
Testing,  purpose  of,  144 
Theoretical  head,  63 
Theory,  corrected,  82 

defects  of,  79 

discrepancy  of,  78 

value  of,  84 
Thrust,  30 

bearing,  36 
Torque  exerted,  60 
Total  efficiency,  55 
Turbine  pump,  definition  of,  1 

introduction  of,  10 
Type  of  impeller,  18 

effect  on  efficiency,  114 

values  of,  138 


Vane  angle,  values  of,  84 
Vanes,  backward  curved,  69 

construction  of,  172 

curved,  10 

effect  of  number  of,  79 

half,  18 

of  mixed  flow  impeller,  174 
Venturi  meter,  148 
Velocity,  absolute,  45 

relative,  45 

Volumetric  efficiency,  55 
Volute  pump,  2 
Vortex,  forced,  50 

free,  52 

W 


Water  horse-power,  54 
Water  seal,  22 
Water  vapor,  effect  of,  42 
Waterworks,  165 
Wearing  rings,  22 
Web,  16 
Weir,  148 

Whirlpool  chamber,  3 
Worthington  pump,  dimensions  of, 
89 


14  DAY  USE 

RETURN  TO  DESK  FROM  WHICH  BORROWED 

LOAN  DEPT. 

This  book  is  due  on  the  last  date  stamped  below,  or 

on  the  date  to  which  renewed. 
Renewed  books  are  subject  to  immediate  recall. 


27Feb'57PW 

REC'D  LD 

26Feb'59jP 

REC'D  LD 

F£B  2  7  1959 

ISAor'fiifr 

REC'D  LD 

APR    4  1961 

NOV    41978 

REC.CIR.OCT  I7  '78 

LD  21-100m-6,'56 
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